Corsair Attack and Army of the Dead

But Isengard's fall would have important impacts due to its contents. The Star of Elendil among other important objects were held there. The impact of this is it allows him to more legitimately claim to be the "King in the North". Which would make the Paths of the Dead easier. On a more personal level, there is Arwen. Until Aragorn unites both former Realms in Exile, Elrond would not grant permission for the two to marry. This would prove to be a vital element in completing this. Which in turn made it much easier to establish a new royal line after the Return of the King.
One possible solution to the Easterling supply issue could come in the form of the Corsairs moving supplies from their farms north via the same river. But that would be problematic too. Replace Cair Andros with Pelargir and you get similar issues. If they can’t crack the defenses there, they are forced to go over land and their main advantages are sacrificed. Not to mention they might suffer from their own logistical issues if they are not able to transport goods via ships. The Haradrim would not be of much help, with their entire economy being essentially foraging.
Aragorn's route to Minas Tirith goes through the Southern Fiefs and pulls off two major feats that would solidify his support from the nobles. First, gaining the Army of the Dead would have profound impacts. It demonstrates his legitimate claim to the throne and gives him the military power to defeat Gondor's enemies. The second is just as important. The first demonstration of this military power is the destruction of the Corsairs as a threat. This shows that Aragorn is willing and able to use this power in a way that eliminates the overriding concerns of the Southern Fiefs. The result is that they would likely answer his call for more troops and by doing so making him the de facto ruler of Gondor. It would take other symbolic acts and military victories before this becomes official. But for all practical purposes, Denethor would have been replaced by Aragorn prior to Aragorn even getting to Minas Tirith. Perhaps Denethor's concerns were somewhat justified. This would present an opening for the White Council to resurrect the line of the Kings.

The Conflict

Deployment

So - there is an important thing we need to get to here. The speed of the Southrons would directly impact the battle. Here is the thing - the Corsairs were heading from the same area and had the benefit of water transit. So it seems weird that they would get to Minas Tirith later than the Southrons. Generally speaking - when two groups are using roughly similar paths, the one with the boat wins any race. Which means the two would likely be travelling together or the Southrons would arrive later. So when the forces of Mordor arrive, there would be no Corsairs or Southrons. Just the orcs and Easterlings would start off.
But one thing that might prove problematic is the presence of the Ring Wraith from Umbar. Naturally, he would be moving up with his forces. It would also make sense to me that he would be the one to order the transportation of the ships over land that I will get into later during the main battle. But one thing that Aragorn and company would not be expecting would be the fell beast. When Aragorn attacked Umbar, things were still in the covert phase, where both sides were prioritizing stealth over power. At least more so than either would be at this point. So the Wraith would be in possession of a fell beast and be openly using it.
But we have a problem. The Southern Fiefs. A huge chunk of Gondor's military power comes from here. But the River Anduin is the path the Gondorian troops reinforcing Minas Tirith would take - and the one the Corsairs and Southrons would be moving along. Given the huge numbers of troops that are already at Minas Tirith, it seems unlikely that the Corsairs and Southrons would add too much. Oilphants and ships do not help much anyway in a land siege. Remember the whole logistics issue that led a lot of real world besieging armies to actually surrender first? The massive resource demands of the Oilphants would only add to this.
Gondor would have a decent amount of troops in the area. Once the Southrons and dwarven mercenaries leave the southern border walls, the professional troops in the area would know the game is up. Pelargir would be a much more defensible area and also is highly strategically valuable. So the former border guards would probably retreat there. The 25,200 men of the Compagnie d'ordonnance would be deployed in the area specifically to deal with this threat. Many would probably be held back to defend local manor houses and castles in the area. But the rest would be naturally sent to defeat the invaders. So I estimate that roughly 16,800 would be sent in.

Battlefield

Now, the Corsairs could prove quite useful in moving up the river to break the deadlock at Cair Andros. This would allow the Easterlings to get their supplies moving again and provide extra ships for that. Plus, they would probably use their plantations to provide supplies to those already at the city. As they move up to Cair Andros, they would drop off the needed supplies before heading on.
But there is a problem with this. The chains across the river. I suspect that both Pelargir and Osgiliath would have these chains blocking the approach of the Corsair ships. Which would mean that the Great Ships might be blocked. But there are two problems with this. First is the Great Ships might be able to break through the chains involved. This would allow for them to continue up by river. The second is the impressive size of the Ottoman ships. You know - the ones they successfully carried across land to bypass similar defenses.
This is where Aragorn's raid might actually come back to bite him. The more of the Great Ships are destroyed, the more successful one can say his raid on Umbar would be. But there is a downside. This would force the Corsairs to conduct their invasion with just their longships. These are much smaller, allowing the "carry over land to bypass naval defenses" idea would actually be easier. But naturally, this would be slower than simply sailing. So we still have the time element playing into Gondor's hands.

The Engagement

The chains forcing a slowdown of the enemy advance allow for two things. The most important is it would slow them down long enough to become a problem in terms of supplying the Easterlings. Especially if this idea is not figured out fast enough. No one would jump straight to this idea because it is counter intuitive. Meaning that at first there would be the normal attacks aimed at storming the towers holding the chains.
Should this fail, they would then probably start raiding the surrounding territory. This allows them to bypass Gondor's superiority when Gondor is defending in a siege. Meanwhile, raiding plays to their strengths and what they are used to doing. Ideally, this would bait the defenders out. But failing this, they would then attempt to carry their ships after an enterprising captain (or the Wraith) gets the idea in a moment of desperation. But all these steps take time.
This leads to the second thing. If these slow downs are bad enough, it traps the Corsairs for a critical period. It would allow the Southern Fiefs to mobilize their forces and more easily defeat the sea power on land. Something the Southern Fiefs would be relatively well equipped to handle. After all, this is a threat they had been dealing with for a long time. Then, with the Corsairs trapped at Pelargir, this would make Aragorn's attack with the Army of the Dead much easier. Namely because he would not need to march as far and the fighting would telegraph their position. The result is the temporary slow down would lead to catastrophic defeat.
But the Southrons would provide no real benefit at first. Well, at least at Minas Tirith itself. In the terrain to the south along the River Anduin, there would be much more use for them. To me, the Corsairs and Southrons would be intentionally left to raid the Southern Fiefs from the river and block troops from here moving to the city. Thus Minas Tirith would be cut off from the rest of Gondor.
When the supply issues due to Cair Andros start to cause problems, the Corsairs would be sent up as fast as possible. The Southrons instead would be left to act as a rearguard. They would move up the river towards Minas Tirith, making sure no one is able to attack from behind, especially by surprise. They would most likely be raiding and looting the whole way.
This plan would help justify the absence of the southern troops a bit more. But now we start getting into timing here. Part of the reason the Corsairs were not an issue at Minas Tirith itself was the Armies of the Dead. They showed up and wiped them out. Which then allowed Aragorn, the Gray Company and the Army of the Dead to move up to Minas Tirith faster by taking the captured ships. The Corsairs in my plan would be taking a much more leisurely pace, so they are actually more exposed to Aragorn's surprise attack here.
The problem with the new plan I came up with here is that the Southrons would be wiped out at the same time. But lets be honest here. Like the Spanish Inquisition, no one would expect the Armies of the Dead. So the fact that there was no plan to deal with them is not a shock. Mordor in fact is completely justified in not treating this as a serious threat. After this battle, we can not grant him that benefit of the doubt. All this to say that this attack cannot be expected or prepared for. Which then leaves this modified battle plan the best based off available information to Sauron.