I probably should have caught on sooner, when others noted that they had to use the "T-Mobile" (WAP) browser instead of the "Internet Browser".... Turns out the real fix is a bit more subtle than that.
I had this working once, and then for some reason, it seemed to stop working. I would get the media player open and see "Loading..." and the video would never start. I even made sure that I was trying via the "T-Mobile browser", and that I was surfing to "m.youtube.com". Still no joy...
Then I got curious and edited my bookmarks from within the "T-Mobile browser". Specifically, I looked at my "youtube-mobile" bookmark, and found that the bookmark definition itself called for use of the "Internet browser", even though I started the "T-Mobile browser" in the first place. Seems that individual bookmarks can "request" the services of one version of the browser or the other, regardless of the browser you were in when selecting the bookmark.
It also appears that both versions of the browser share the same set of bookmark definitions.
So -- I changed the browser setting on my "m.youtube.com" bookmark to specify the "T-Mobile" (WAP) browser, and lo and behold, it works beautifully once again, regardless of the browser I'm in when I select the bookmark (since the bookmark itself forces use of the T-Mobile/WAP browser).
Subtle, but it seems to have fixed my issue with mobile youtube on my 8900 (and, btw, I'm running 126.96.36.199 at the moment).