Honest question... why not just get some sort of excuse to be able to sleep at those times when you are ready to sleep. Sure it might be during "working hours" but if that is when your mind decides it wants to sleep then for purely health reasons doesn't it make sense to seize that moment and sleep? Would you sleep for hours at that time or would you just wake up in an hour? Either way I can see scenarios where this could work.

I can sometimes get 20 minutes at work but there are few private places where this is possible. I got a 10 minute nap once and woke to find two very concerned people wondering if I'd had a heart attack or something!

If you haven't experienced insomnia it is, like most maladies, far more complex and difficult than you might imagine. Everyone has a suggestion or two, but it differs for each individual and has a multitude of causes (as I hinted, in my case a heart problem plus various complications from that, which I hope to get sorted soon).

That would be an awesome thing to be allowed to do. Outside of high workload Asian offices I haven't heard of sleeping during hours was anything but firing material.