Howard,
Thanks for the very quick reply.
As I've been removing the old floor, I've already been able to remove one strip of the old foam uderlayment, confirming that it's not attached to the piece next to it.
Also, its the same color on both sides (white) and does not pull apart. It resembles foam you'd use to wrap something fragile before shipping it. Actually, come to think of it, its nearly identical to the sheets of foam they put between the EasiKlip boards in the box. For kicks I took the piece and cupped it and poured water in to the cup and it did indeed hold.
However, I will take your advice and go for the 2-in-1. My resistance has been the fact that this is a very small apartment with a ton of stuff. I had figured out a way to install the floor by moving all the furniture to one side, then moving it back and installing the other side. I think this type of moving operation will be difficult with a large sheet of plastic, and would also risk ripping it, so we'll have to figure out somewhere to put the furniture. This adds considerable complexity to the job.
Thanks again for your input. It's much appreciated.
-Rick