Take it all out down to the original subfloor.
How long do think a person can continue to heap floor covering on top of floor covering on top of floor covering before it begins to effect a new floor covering installation?
Chances are there is asbestos containing products buried down there somewhere. So what? If you don't sand it and don't grind it and don't crumble it and use it on your breakfast cereal, it can be removed with little to no concerns.
REMOVE THE VINYL(S)