There are some really good epoxies made that would probably adhere better and be cheaper than trying concrete. I'm not an expert, but doing concrete might be a bigger deal than you think if you have any cleanouts or plumbing in the floor.
Personally, I would buy a good mask, water the floor down, seal off the basement room, and remove the tiles. Sounds like there are only 500.
If not, I'd probably just put concrete board or epoxy over the whole thing. If you put concrete board over the whole thing, it'd probably encapsulate, and serve you pretty well. The problem with epoxy is that if you have loose tiles, it wouldn't work.
Go for the concrete board 1/2" thick. It comes in 16 sq ft boards, its heavy, and costs about 80 cents a square foot. You can do the work in your spare time, and won't have to rush like you would pouring a sand mix over the whole thing.