We are almost in the same boat!
First of all, 10 pages is TOUGH. Two of my programs want 15-20, and I've been struggling with that. My advice would be to submit the chapter with a cover page. I once tried to get my 150+ page thesis down to 20 pages, and it's really impossible........you end up losing a lot of the interesting detailed analytical work that I feel they might want to see. So I'd recommend trying to get a chapter down to 10 pages, and include a good abstract. You might want to ALSO submit the full bibliography for your thesis, though I've heard mixed thoughts on doing this. I feel like it can't hurt. (In my case, I'm preparing a 20 page sampling of my thesis that includes an abridged intro, and abridged chapter 3, and an abridged conclusion...this totally omits the 4 other chapters, but I have a summary in my conclusion AND my abstract, and chapter 3 can stand alone, analytically).
Second of all, the unlimited option is also tough. I emailed a program directly about it, because they actually said "submit your thesis if possible" but I doubt they'd read my entire paper or even want to. In response to my email, they said I could either submit an excerpt or submit the whole thing with a cover sheet sorta pointing them to the good parts. Moral of the story is: they are probably not going to have the time to read your full thesis, so give them the best part or point to the best part.
(For this option, I am submitting an edited but still pretty full Intro-Chapter 3-Conclusion from my thesis, which will amount to 40-50 pages)
Do any of your programs require more than one sample? Almost all of mine do. I'm basically writing a new sample and capping it at 15 pages.