I haven't had a chance to run any of the drums I've turned down, but after taking a few thousandths off, I keep the drum in the chuck and run some emery cloth over it while it's spinning to smooth out anything rough that any tooling may have left (I'm using old tooling, and a considerably older lathe....) I don't want a glossy finish, but want to make sure that it's smooth enough that it won't wear a band prematurely. It's tough to gauge what yours look like not having it in-hand.
I'm glad it worked out for you. I'm a hack, and I'm happy with the job I was able to do in about 10 minutes for a couple drums that'd seen better days.