I agree that tile is the way to go but even with a good mastic, if the subsurface isn't solid the new surface won't be either.

rich23s, Home Depot sells a product, it comes in a roll, its orange in color, its flexable plastic, it has little squares imbossed in it.....Sorry I cant rmember the name, but its in the tile and flooring area, ITS slick, put your floor prep down, lay the orange membrane over that, let it cure, come back tomorrow, lay mastic and lay tile.

Their side is all the rest of the test-ready installation (ducts, custom made return w/grill, plenums, and mastic sealants).  

I tried farming out the tiling and just ended up with guys who could mastic something to the wall but couldn't understand how to make it aesthetically pleasing.

I had a pretty tough predicament, a layer of vinyl flooring was glued onto the original floors with mastic. 

That said, the liability of knowing about the presence of asbestos in the living area or HVAC system (ie in plaster or floor tiles, duct wrap/mastic), but not disclosing it could come back to bite you if something ever did occur.Much of our building stock is old here in the east - 1920s-1930s would be newer buildings in some neighbourhoods.  

So I tried removing some of the mastic and glue with Citristrip last night.

Mastic" is a generic term for an adhesive.

I would bet that block was tarred with a waterproof mastic coating before the ground was backfilled around it. 

I've been looking into Mastic and Shirley area but your current about Long Island, tough to get starting in.