I finally purchased an electric heat gun (575 & 1125 degrees) and a plastic putty knife (Home Depot). Using the heat gun on LOW (575 deg), I heated the LDPE to the melting point and then used the plastic putty knife, in a nearly perpendicular position, to scrape the plastic off the...
Opting to keep the tiles as clean as we could and avoiding the float, we used putty knives to get the grout directly into the gaps. We still operated as though it was a float though, pulling the knives diagonally over the lines to minimize the chance of it digging anything out of the...