You might be able to look at some phase change materials that are used in greenhouses. They seem like they might be more lightweight than a brick wall.
But honestly, I would just do what people do for fireplaces and things like that. They build a stronger foundation under that one section. Maybe cement, maybe brick, maybe stone, but instead of wooden piers, you might have like a 6x4 area that is solid (or a wall filled with rubble) under the fireplace. In your case it could be a brick or stone wall of some sort. I think most of the time they build it solid up through, and build the floor around it. In your case, you probably want some sort of insulation break between the support and the actual mass in your house... but then again, maybe not. That piece would be beyond my experience.
I think I might go this route. With our very temperate climate, a fireplace or 2 is more than enough. Especially in a properly insulated house.
A quarry tile floor would add a bit of thermal mass.
Nice, hadn't thought of that one. We might be able to have a small section of quarry tile in the right spot to pick up some warmth
I assume you want the mass as a cooling factor?
Make the walls thicker than normal walls.
Make the walls out of concrete blocks [the hollow kind] or adobe bricks.
What kind of cellulose? Paper might be lighter than sawdust.
I want the mass to regulate the indoor temperatures. While it is temperate, we do have major swings to either extreme every now and then and they're just getting worse. Walls will be plenty thick cause we're building out of strawbale.
The cellulose we have available here is paper so works in my favour.
With a foundation of wooden beams on piers I worry about overloading it, especially as you are on a slope. Please consult a structural engineer!
That said, have you looked into the feasibility and potential effectiveness of doing a water wall? Basically a large water tank built into a south-facing wall, typically below the windows; it acts as a thermal mass. You might even be able to do this underneath the structure between the piers.
We were looking into incorporating our water storage and thermal mass into one system, but abandoned the idea because the engineering looked a bit more involved than we're going for. Might revisit this one though, thank you!