Game physics is not affected by FPS in this game, so you can't achieve Faster Speed by uncapping the game engine, doing so will make everything go faster so it is just pointless.
However, strafe-jumping is a very effective way of building speed when done properly, that means, start and press shift(run) and jump at the same time, release shift, add strafe key, as soon as you land, press shift again and blablabla, although on DOOM3 the strafe jumping needs the A or D keys to be already pressed when pumping each jump.
If you manage your stamina correctly most of the time you can survive half-way through a level with it, so I suppose on a TAS that would mean almost all the level.
Grenades jumping, rockets jumping & Barrel boosting also works but need the exact timing and angle for them to works and an unpatched version of the game (Doom 3 1.0).
It is possible to do them on Nightmare difficulty even if it seems impossible to pull off.
So far that is all I can think of, and I have been following all of doom 3 run on SDA since 2006-2007 so you can trust me on my word.
You can also use the game engine to make demos and slow down the game using console VAR, as I did way back for shortcut searching for Kibbo and Tagh_Azog...(IIRC)
Demo Function is broken in the game and does not record any GUI, if that could be fixed though, the demos command would work extremely nicely for a TAS.
EDIT: Anyone wanting to do a TAS for this game should aim for something like 1:04 or almost sub 1 hour.