Sorry I couldn't reply to this earlier but I can help. I still play TS2 regularly and have experienced exactly the problem you've had when I first tried to play it on a modded console.
The reason is Timesplitters 2 is one of a handful of PAL games which don't support NTSC display. There's no point in fiddling with the NTSC/PAL UnleashX settings they can't help in these cases. Similarly ripping the game to the HDD won't help either.
You need to use the Enigmah region changer app to swap the console back to PAL.
Also, maybe of interest, there are some games: Panzer Dragoon Orta and Gun Valkeryie which previously I'd assumed were in the same PAL only category. But I was wrong these are in a unique class of their own in not being playable on a v1.6 Xbox in 480p. I'm not sure if this applies to US NTSC game versions.
What this means is that if you have a modded PAL v1.6 console region changed to NTSC with 480p ticked using the MS or UnleashX dash and Component cables those games will not display properly. Change the setting to 480i and they will.
Aparently this is down to the Xcalibur video encoder used for v1.6 machines. Earlier Xboxes which used a different encoder can play the PAL versions perfectly in 480p.