I feel like your full body work out is not sufficient to really hit any one muscle group, so there is no concern of overworking. "A set of bench press does not a chest workout make." I'm sure some wise man once said that. Whether it be the upper/lower body split as recommended above or a more conventional routine that might require you to bump your classes to make room for another standard gym day (you can always switch 4 or 6 months on straight gym bulk time, followed by equal time back with your classes on a cut), I think it's clear you should be targeting muscle groups more effectively to actually require that rest period before your next work period. I don't know that your work-required training will necessarily interfere with any heavy weight training on the other days. Ideally the muscle groups would be resting, but it doesn't sound like you're asked to do any hardcore muscle fiber attacking, so I don't believe it would lead to over training or limit your gains.
"I am all that is Man!"