Hey there -- I'm not a ceiling person but I have tackled stucco and popcorn ceilings two different ways. #1: The drop ceiling grid (as people have mentioned and you mentioned) is relatively easy, affordable and not messy. You will loose anywhere from an inch to two inches for the drop grid and of course you have to buy the framing and tiles you want. I've done one ceiling with black frames and high-end marbled acoustic tiles (also including lighting) and I've done a huge basement with silver framing and tin tiles -- both fabulous. #2: Cheapest and quickest way to cover popcorn is paint, paint and more paint. I would use a large nappy roller and lather it on, two heavy coats and maybe a third. The popcorn effect will diminish with each coat. New drywall is the absolute best and most comprehensive fix. I would investigate, however, why the popcorn finish was used in the first place (very important). Often this technique is used on uneven surfaces, really large areas, commercial use areas, track subdivisions, etc. I'd advise you against knocking off the points with either scraping or sanding. You will experience chips and clumps falling down. Popcorn finishes have a composite mixed in with the paint for adhesion to its primary surface (either vermiculite or polystyrene). Once you start the chipping or sanding you will have to go down to the bare, bare surface and then patch, paint anyway. Going completely over what is in place now with a drop ceiling or paint -- or pulling the primary surface down and dry-walling is they way to go. Even nailing into that textured surface or trying to "glue" something to it will cause the cracking, chipping, clumping and it will not be secure. My two cents -- good luck.

Depends on where you live. Contractors will probably charge you $1 to $2K, depending on how many rooms. I actually had one contractor who suggested adding sheetrock over the popcorn ceiling -- for the bargain price of $20k (they were union contractors so that should tell you something). I've seen some GREAT ways to do yourself online (shop vac is my fave), BUT then you've got to figure out what you are going to do next. I know everyone wants a "smooth" ceiling but it's a lot of work to get it to look like that after you remove the popcorn so you have that as an added expense. So make sure you calculate all the expenses of your ceiling project.

Isn't the whole point of sending off the sample is so that you could get a result that would help determine how to proceed? If you aren't going to trust the result, then why bother to send a sample? But since you do doubt the results, you could always send a sample to a different lab for reassurance. Or, you could hire an asbestos abatement company to come in and remove the popcorn, but it won't exactly be cheap. I removed my own popcorn ceilings and it wasn't difficult. Messy, but not difficult. We then had a drywall guy re-texture them. I did have to hire an asbestos abatement company to remove old venting from my attic when I wanted to replace it with new. It was an ordeal involving men in white hazmat suits and a plastic tunnel constructed between my attic and the truck. I'd avoid that if I could.

You could have a drywall man come and put 1/4 or 3/8 inch drywall over the top, and tape and mud it for you and have it ready for painting. I am wondering if this may be something that is a bit over your head, since you seem to be not used to doing this type of stuff, so may be better to hire someone. If you do that, then watch that person carefully, and you will learn just how it is all done, so if in the future, you get another house with the popcorn ceiling, you will know just how its done. It can be a great learning experience and you may enjoy it a lot too. That vaulted ceiling you have can be a bit of work too, because of the height.