I have never seen, heard of or experianced this issue which makes me think its a hardware issue specific to your xbox, or mod. I doubt its the mod if my 3 year old bigfonts softmod plays everything perfectly. The way the xbox works is every game is designed to run from the DVD drive, so if there were any issues it would be playing from the HDD. You could also try burning the games to DVD+R maybe? You could also try ftping the files off the hard drive and burning an iso with them specificaly.
Normally I would ask for specific examples of games that do/don't work but im not going to be around for the next week, so that would be kinda pointless.