Nice; that was all I needed. A little push into the "winbind" direction, and then I knew what I needed to look for. Got it working now. Thanks!
In case anyone else has this issue:
I had everything configured that I saw online, BUT for some reason I never wrote:
idmap uid = 10000-20000
idmap gid = 10000-20000
These are apparently extremely important lines. I figured they were more of a nice feature rather than a requirement, and that Linux would just designate UIDs and GIDs based on the order it found them. I didn't know it would stop me dead in my tracks if I didn't tell it specifically where to put it.