Thanks so much for the advice, doubledutch.
Now I can stop feeling guilty for using an entire roll of paper towels in one hour this morning! I really hate dusting. I will get some microfiber cloths for the future. You're right. Most of the dust will go down the drain. Some might remain, but it's better than not dusting at all!
I think our vacuum is pretty good. It's new, and it does have a HEPA filter. We fill the bag up quickly, too! But, from what I've read, asbestos fibers are too small to be captured in a typical HEPA filter. Professionals use asbestos-rated HEPA filters, which are thousands of dollars!
Of course, our vacuum probably does capture lots of other bad dust. Which is good, because there is lots of bad dust in today's world!
I would rather have your asbestos tile floor! Ours is actually sheet vinyl with an asbestos backing. The vinyl itself does not contain any asbestos, but the backing is almost half asbestos! Luckily, the backing is covered by the vinyl, so the only way the fibers can escape is along the edges. But we have a lot of edges, some going all the way across our living room. And they are being, walked, run, jumped on constantly by the kids! I'm going to try to seal those edges with something.
Your floor is actually easier to remove than ours, since the asbestos isn't considered friable. Our backing is friable and dangerous to remove. From what I know, you did the best possible thing by painting over yours.
I'd love to get our ductwork vacuumed. It's so scary to look down into those ducts! Have you had that done before?
Thanks again for your help!