The Trireme

What is the most popular way of travelling mid-range distances in your setting?
There is more species of burden beasts and mounts being used at any day on planet Sharitarn than one could mention in one human lifetime, if that entire life was dedicated to read a list. Each minute of it, with no pause for sleep, drink water, or learn how to read. When you reached the middle of such list one in each five species you mentioned would probably be extinct, replaced by species brought by the Vortex while you where reading.
Few are the races trusted by Merchant Caravans that dare to undertake long travels, and those caravans often change their animals several times while travelling. Because Sharitarn wild lands are harsh, and the better way to have a chance on them is to use the mounts suited for the land where you are presently.
A generic answer for the question that is valid for travel through land is: Merchant Caravans. The way to travel mid-rage distances on Sharitarn Continents is to do so as part of a Merchant Caravan.
Either that, or you are at head of an army. It has to be a very strong army however.
Humans do not travel alone on Sharitarn, unless they can't avoid. Chances to reach destination alive are small for those who don't have both powerful magic and great survival skills. Even Warrior Castes don't walk far from their nations very often in groups of less than half dozen men.
Some wild men hunt alone, in some parts of Sharitarn, expending months without see other humans. True, but they only do so in the land of their tribe.
Travel through land is seldom the best option on Sharitarn. If you can avoid that, you will. That leads us to the standard way to travel: boats.
Short distances are made on small rafts and small fisherman boats. Long distances demand a special kind of Ship that does not look much with anything we know on Earth. Between those extremes, the standard option is Sharitarn trireme.
One sail, oars, a few dozen Sailor Caste men and perhaps a Merchant Caste to pay for the trip and bother the captain with suggestions that must be politely ignored for the sake of survival or every person present.

Where to Sail?

Most nations don't sail through Open Sea. When they travel through the coasts that face it they never move their vessels at night, only during day. Sailor Castes don't explain why, just say that is a matter of avoid bad luck. It really is, if you count be eaten alive by intelligent octopuses as bad luck.
Some few nations have deals with the octopus people (Mimbao for instance). More precisely some lineages of sailors from those nations have the mentioned deals. Ships of those nations sail through Open Sea, and do not stop at night, evidently, but for that they must have a member of the families on board.
However, Open Sea is dangerous enough without the octopus people. The Sorrowful River is the best route for travel. That and the actual rivers on the continents. Also lakes.