I agree with your call of bollocks on the 'trainers'. Your "stamina" will be fine from the frequent boxing practice, as well as from the soccer (err...football, whatever). With limited training time, you really want to stress basics, basics, basics. I'd definitely go full-body both days. Probably using the same exercises, but different set/rep parameters.
Two top notch moves for martial artists (and technically, boxing is a martial art) are cleans and full contact twists. Find a way to include them, and you're mostly golden.
Alas, the foul concept we call reality tries to spoil an otherwise perfect suggestion. But I'm not going to let you off that easy.
I really want to see an overhead press in there somewhere. I recently brought my weights down into the basement, from the outside garage. The ceiling is just about 5 inches above my head, so I'm in a similar situation.
What I do: 1 - Clean the bar (a power clean from the hang is fine). 2 - Take a step back, as in a reverse lunge. 3 - Quickly step back with the "forward leg". You should end up with both knees on the floor, thighs pointing mostly straight up, and the bar still in the rack position. 4 - Proceed to press. When your set is done, dump the bar forward to the floor. It takes a bit of practice, but I think overhead pressing is worth the time and energy. Plus, that whole series by itself is a wicked little complex (clean, reverse lunge, press). Bonus points.