I wish I could take naps during the day when I get fatigued, but unfortunately I have severe sleep apnea, so unless I sleep with a CPAP machine, I don't actually get any rest. And my CPAP machine isn's something I can bring to work.
"http://www.cpap.com/productpage/z1-travel-cpap-machine.html"
I understand you still need a mask with these but it might be worth considering depending on where you can situate yourself.
You can use it for travel and vacations, but the best reason to have one is as a backup. Trust me when I say that you don't want to wait a month for a replacement when your existing CPAP fails (and it WILL fail).
Also, it's worth noting that many travel CPAPs have 12-volt car lighter adapters so you can run it off of your car's battery. So maybe you could use it to nap in your car?
Prior to that I had found a site that specialized in used cpaps and they were going to buy it (apparently they had so much inventory they wanted to wait to make an offer on it).
You can probably source a good used one through respiratory therapists either privately or at a hospital. When someone passes away these are typically thrown out. (After a certain amount of time they don't get returned to medicare or something like that.)
(To be clear, I'm not suggesting you get "all lawyered up" and obnoxious. Just ask for a meeting with HR, to discuss ways to make it work for both of you. Pointing out that you use a medical device should help get across the point that this isn't a frivolous request to doze.)