In general, I've found the biggest obstacles are social (i.e., people think you're lazy), not logistical. But these are largely gone for me now that I'm running my own company. My cofounder and I have vowed to not just tell any future employees that napping is acceptable, but to actually keep doing it, so they see that we're serious and feel comfortable napping themselves should they want to.
I'd recommend telling your coworkers/boss that napping makes you more productive, and that you only take one 20-minute nap a day. If they're silly and care about exact minutes worked, just show up a few minutes early or start a bit later.
Genuinely curious: How much of the sleep deprivation is due to employment practices, and how much is due to, say, American cultural values? Are we sleeping less because our employers or our social lives demand more?
But some are lucky genetic mutants. I am not one of them.
Options here are obviously, book a meeting, pretend you're going for a run, out to lunch or a coffee.