Honestly, here is how I deal with this. My bedroom is full of computers, and while I keep most of them off during the night for noise reasons, if my rabbit, which is in the next room, starts going nuts for an extended period of time, I will turn some more of them on just to get the idle noise (and believe me, two 7800GTXs, an FX-57, and 4 7.2k hard drives and you couldn't hear the world ending past that.
I was in a situation where I was sleeping in a hotel room on my way back from Germany (we stopped over in Boston) and I am a rather particular sleeper. There were two beds, and four people, so naturally I just slept on an armchair, which honestly wasn't that big of an issue. The issue is that half of the people in that room snore like freight trains and no matter where I went in the hotel room, I couldn't get away from it. So, my best solution was to put on my headphones, connect it to what was an iPhone 3G running whited00r at the time (My first smart phone for use as a simple PDA I got for 30 bucks), and then just play music for the entire night. I didn't have much (like 12 songs) but on repeat it was enough for me to fall asleep and moderately annoy everybody else in the room as they weren't really good headphones and sound bleed was excessive even on lower volumes (it was a fun vacation).
I also used to just play the radio at night while I slept. I haven't intentionally tuned into a radio for years, but that was fun while I did it.
I know you said no headphones, but I would give it a try. If you like earbuds, then you're golden as those are perfect for sleeping. I can't stand earbuds so that's a no go for me.