Hang new drywall. It'll be as quick, if not quicker than anything else and you'll get the best possible result. There's nothing special about the drywall that came with the house. I do drywall estimating, I would charge less to demo and hang new than I would to do any of these other options.

If the texture is deep, floating it out is going to be a pain in the ass, same for sanding it flat. You're right about it pulling the paper off the drywall if you try to remove it. Putting 1/4" over the top might result in it being lumpy if they don't knock it down to being semi-flat AND like the other person said, you'll have to deal with outlets and light boxes being buried in the wall. 1/4" is usually more expensive than 1/2" anyway.

While you've got the drywall down you can put whatever outlets you could dream of or lighting in easily. Maybe a heated towel rack or an in wall medicine cabinet or sound insulation. Throw in a new vanity while you're at it,... Instead of just paying to get rid of something you don't like about your bathroom, do that AND add a couple things that you will like.