I would go to a pro flooring store that sells armstrong and ask if armstrong s-1840 floating underlayment can be used after peel and stick tile is removed. I know it can go over regular floor tile glue, they just trowel over that with Tec 200 self level, let it dry, sand, throw the 1840 and armstrong lux tile down. S-1840 is only .040 thick and comes on a roll, ours has been flawless for 10 years, on top of 1950s sticky black tile glue. I know there is an issue with some pressure sensitive glue and they replace the whole subfloor.