I think you hit the heart of what can become trade-offs when you're an elite athlete: sleep, training, and everything else!
I also find getting out there makes a positive impact on how I feel, and even as a recreational athlete, I'm protective of my training time.
One approach that has worked well for me is to see where I could work training into activities I already had to do (and thus win back some more sleep). In grad school, I got a locker at the student center and stashed clean clothes / shower stuff, and then I could run from home to class. Plus, I had some unexpected speed training on the days when I left a bit late.
I got to do that a lot living in DC, too - run 5-10 miles to work, take public transportation home. And when Jon made a sprint map of our development in DC, I would run home from the metro stop a mile away, grab a map from a stack by the door, and go work flow by hitting 5-7 quick controls. 20-25 mins from metro door to shower, speed work, and map time.
It can't all come at the cost of sleep, though. In Iraq ~(4-5 hours of nightly sleep for a year), I saw a real decline in my running performance as my reserves got depleted. It also got really hard to think clearly when I was so tired. Conversely, I've slept as much as needed over the past year, and I find that my ability to hold focus through a long event is much improved, even over just normal life with family and job.
All that to say I hope you can find some creative ways to work in training, while making sure you get the sleep and study time you need. Good luck!
Thank you for the suggestions! I do try to work in at least a little bit of training where I can -- typically for me that means running errands while actually running.
Literal errand running. I love it!