Laurie-
As you surmised, pouch advancement removes that troublesome bit of rectal cuff, and the pouch is then hand-sewn to what remains. Mucosectomy is the removal (essentially scraping, I believe) of the innermost layer of the remaining outlet, which is also prone to UC. Mucosectomy carries a higher risk of true incontinence, wich is why it now isn't routinely performed in the first place, but many folks here have had successful mucosectomies.
IMO pouch advancement should only be performed by a very experienced surgeon. The hand sewing is delicate, and mobilizing the pouch is tricky, too. If I needed it I'd simply go to Cleveland, unless I had very good evidence that my local surgeon had the necessary experience and success.
A Crohn's diagnosis might change things, though. I had J-pouch surgery with a probable Crohn's diagnosis over ten years ago, and I knew what I was doing. Several surgeons turned me down for a J-pouch, and the odds were certainly less favorable, though things have turned out even better than I expected. The story is likely different with pouch advancement or BCIR, both of which may simply be a bad idea if Crohn's is confirmed. In particular, pouch advancement seems best suited to people whose problems are limited to the rectal cuff.