Plumber came by at about 8:30. Once again a dispatcher FAILed to give my very simple directions so it took him 10 minutes instead of 3 to get to the house from the front gate. At least they gave him the gate code.
Long story short, in order to install the kind of sink I want, he needs to re-pipe the whole shebang. They have a coupon special for the disposal.
Showed him the toilet, he agreed that the problem was the toilet itself, and maybe some calcification in the pipes. He used his big snake to clear the clog. But the main thing is the house came with water saver toilets. So in addition to the sink and disposal, he'll be putting in an ADA-compliant, high volume throne. It's looking like close to $2k. All day project, he needs to get a sink & toilet and will be back Sunday.