You may find this a bit weird, but I handle stress from work by listening to music on the way home (sometimes in the morning as well) and... singing along.
(Yes, even rap)
To be honest, your predicament sounds similar to mine. Our workloads come in waves, so it's either all hands to the pumps or we do other things, like shore up on systems training (which usually falls apart because by the time we get to scheduled training time, something's come up).
However, my company hasn't got any hold on me in terms of education and my boss knows this. So I do get respect. On Tuesdays. Between 10 and 11.