You may wish to spend some time over at
www.builditsolar.com, tons of great ideas there.
I'd use two layers of glazing, Glass on the inside (cheap, high heat-resistance, perhaps an old sliding glass door?) polycarbonate on the outside (good heat-resistance, great breakage resistance from branches, etc). I'll bet your plexi will half melt fairly quick. You will be suprised at how hot the collector gets.
For thermal mass, a dry-stack of masonry blocks absorbs heat quickly, but water drums will hold 5-times the BTU's per volume. On a cold winter day, if the sun only comes out for a short while, you need to absorb as much as possible as quickly as possible. Water drums absorb very slowly, but hold more BTU's.
A hybrid pile has been suggested to me as a cheap and useful option. The top half is water drums, and the bottom half is masonry block. During the day, the masonry absorbs whats available quickly. At night, the circulation stops and the masonry heat migrates to the drums above overnight.
In dry winter air, mold and fungus is not a big problem, but in cool but humid air the stack can get funky. In that situation, you can seal off the solar collector and heat-storage pile into a closed-loop, you can draw off the heat from the top of the pile by inserting an aluminum heat exchanger, such as an 18-wheelers turbo intercooler. Its a large aluminum air-to-air radiator.
More complex, but that would also allow your system to passively collect any time heat was available, but then you only draw off as much as needed from the storage box to keep the room comfortable.
Install one-way flaps on the bottom ports of the collector so at night it doesnt reverse flow and pull warmth away from the house.