Is it possible to go to fight Tyranthraxus when you feel you can win? Or do I have to wait until I get the commissions to storm the Stojanow Gate and then take the castle?

I would like to just end the game once characters reach their max levels or close to it.

Tyranthraxus can be fought whenever.

In fact, this is the only time in the Gold Box series that you can simply go fight the final boss whenever you want.

So, does that mean that a speedrun would look something like this?
1. Create party
2. Get the minimum amount of power needed to beat the game (XP, items, etc.) as quickly as possible (or are there some really good (from a speedrun perspective) items that are easy to find?)
3. Go and kill the final boss, ignoring the rest of the game

Should be possible. I did a Pool of Radiance Ironman playthrough (I believe I am the only youtuber who has done this run as of 2016), so I specifically chose to avoid certain fights and zones.

I screwed up on my execution of the last fight, but I believe with the proper use of the Dust of Disappearance, it is possible. The Dust is in the Temple of Bane mission.

Excellent, that's good to hear.