[prairieschooner]

thanks, I would bet that the polyurethane would stick well to the linoleum and it would be much safer than removing the linoleum, asbestos and all (PS please wet the "paper backing" on the older linoleum to keep the asbestos from becoming airborne).
I'll give a spot sampling before going through the entire floor.
As a side note; a small Ball Peen Hammer is a great tool for sounding. As Erniee recommends a probe (I would suggest a dulled Ice Pick or Awl) could also help identify soft spots.