Yeah, I get tendonitis and use these to help alleviate the symptoms. They tend to work out pretty well, although I don't know if that experience would change if you didn't have a full hand.

I agree that using the mats would be the cheapest/easiest option. That said if you want a more permanent solution you could get a poured epoxy floor installed. It can be used over asphalt as long as it has a good base, ie does not have issues with settling/shifting, and it provides a durable long-term flooring solution. Of course, it is expensive and I would highly recommend you pay a company to do it rather than DIY.

OP should still test it. When I was working doing gut jobs on old houses we found out a lot of popcorn ceilings from the mid to late 90s still contained asbestos. Just because the EPA mandated it doesn't mean people stopped using/buying old stock and using it anyways because it was cheaper/easier. Not worth the risk of future lung cancer IMO, especially when testing is relatively cheap/easy.

If it is structural you probably shouldn't use drywall screws, especially in an area that might get wet. They may be the cheapest but they are also very brittle and prone to corrosion. That means that they are prone to snapping if there is a lateral force applied to them, and they will rust through after a couple of years of being exposed to the elements. For non-structural, interior, applications I have had fine luck with them though.

That said I usually prefer to use coated construction screws for everything. A youtube channel called project farm, highly recommended btw, tested all the screw varieties and found that the cheaper construction screws actually outperformed the more expensive specialty screws in almost every test. They aren't that much more expensive than drywall screws either.

Link to the video in question if you are interested.

I get that a lot but it is usually caused by dehydration/heat/standing up too quickly, always a fun time though.