Well, those who said it looked like a twist-off were correct. I was reluctant to be as forceful as I needed to be because last time I forced the plumbing, I caused a lot of damage. Oops. Anyway, the plumber made me sign a waiver saying that they were not responsible if he broke it with his channel-locks. He did not break it, but says that I might just want to take the damn thing out and use, as needed, a hair strainer or one of those rubber drain stoppers as the body of the stopper takes up like half the drain hole, so it will always be kinda slow. (He did clean out a bunch of hair and whatnot.)
It would normally have cost me $224 dollars (yikes) but they waived the $45 service fee because they sort of missed my appointment yesterday and had to reschedule. Then I had a $60 off coupon, so it was "only" $119. At least now I know how to take the damn thing off.
Thanks for weighing in, everyone! Sorry if I disappointed anyone by giving up and calling a plumber!