Since using cut foam was out, I went with a cardboard structure to support my upper level. I still don't know if using so much cardboard is normal. As long as I seal everything down the road, I can't see any downside to it.
I cut a section of cork board, the same material I used for the ramp, to support the 2" high portion; later I'll build natural-looking slopes from plaster cloth. Since the cork board I have is 1/4" thick, I cut out reasonably level strips of 1 3/4 tall cardboard to support it and glued them to the bottom of the base.
I laid out the strips of board without any specific plan, just wanting to support the board evenly. Having them folded seemed like a good way to add stability. The corrugated bits are running vertically. I weighed down everything with some heavy textbooks, which also flattened the board on the table.
After this dried I placed it on the baseboard and glued and weighed that. Once everything was dry, it certainly felt like a strong surface. I wouldn't start swinging around the layout while holding it, but it doesn't budge when pushed on. Also I can easily pierce it to run more feeder line, or trim off sections to better shape the hillsides.
Overhead view without the upper portion of the track in place. Lots of room for the small, rural passenger station that will be going on the spur to the right of the image.
Our cat seems pleased with the whole thing. You can see the wooden bridge, still unfinished, in the spot where it will eventually be fixed. Next comes laying the rest of the track, then fitting the bridges. Soon I'll be receiving shipment of new structures: the station, a signal box, and a small office.