That REI tent is a nice design, similar to its original Quarter Dome, but 4 lbs?
There were 1p FS tents under 4 lbs around 30 years ago.
Figuring that a lighter 2012 model CS 1 floor averages a little under under 3' by 7.5', so is well under 3 sq. yds, you could make a footprint from 3 yds of 3000 mm HH silnylon from T-H, and still be well under 3 lbs. Or you could do the same thing with the 1 oz black or 1.43 oz OD Cuben from Zpacks, only much more expensive, with the same result. Even a footprint from the 2 oz. Tyvek available from Zpacks and other vendors would not take you much over 3 lbs.
Sounds like you just don't like footprints, regardless of weight. You could use the above materials to make a floor cover to go inside the tent. The best way to make it stay in place without permanent bonding - that would take some thought. Maybe some stick-on thin Velcro patches. The Cuben or the Tyvek would be less likely to bunch up. If you choose the heavier weight Cuben (heavy only in terms of Cuben), would love to know how it holds up to Fido.
Caveat: In the past, BA weights given for tents have been lower than actual. Don't know if they've gotten over that or not.