The outside of our house is covered in Asbestos tiles, but we can't find a dump in MA that will take the asbestos if we take it off (with protection).

I had those too. They sided over them because they said, that was less dangerous than removing them.

Asbestos shingles are not friable type. Double bag them small amount at a time and put them out with trash. When they landfill asbestos it goes in the same pile as everything else it just costs more. There are people out there that would take them for their own houses if you can remove them without breaking them. Many people side over them. It is more work, but you won't have to take them down.