I have a 7 week old daughter, and I don't know sleep, either. I also work 2 jobs and am in grad school full time for my DPT degree.
Pray for me.
Seriously though, I have been a personal trainer for four years, so I can always find time to be in the gym.
I've found that Power Drive first thing in the morning with a big cup of green tea 30 minutes before eating breakfast makes my life a lot easier. I also use ZMA while keeping a near perfect diet (one has to when sleep is compromised as much as a little bundle of "joy" can bring late at night).
I'll tell you man, the first week and a half to two weeks were an adjustment period for me. I didn't work out at all because I was just too goddamned tired all the time.
I'm better now, though. I've noticed I need significantly more sleep when the training is at a higher volume and has any eccentric emphasis. Try doing o-lifts at the beginning of the work out, and then choose a movement plane (i.e. horizontal push pull for rows and bench) and go heavy with low volume. I haven't gained really much size, but strength (amazingly)has improved with limited sleep.
In relation to your recovery questions, yes, contrast showers do work well. If you can abuse your gym's showers, take up two and jump from one to the other (You'll get some absolutely INCREDIBLE looks from perople). Sled dragging also helps. I've put a tire and 3 different sledgehammer sizes in my backyard to facilitate recovery and get some cardio in.
A major portion of my recovery has been power drive. Taking that 90 minutes post workout is great. Mix that on the REALLY bad days when I just worked out, didn't get any sleep the night before and need to function fully to understand what's going on in class, I've had great luck with piracetam and / or phosphatidyl serine with the Power Drive. It can get expenive, but I have found my ways. Lemme know if I can be any help to ya brotha.