I think basically you're right about the foam and the RC can's temperature servo. Although the impulse response of the can to heat is fast, the cool down time must be slow as its dominated by the conduction through the foam. Since this makes the servo asymmetric, it cannot have a high gain at the 24-hour period, unlike the system at the 40m.
So, what's the answer? We need to be able to keep the 24-hour period to be less than 5 MHz in the relative frequency shift. Ignoring the effects from the coating we ought to get ~150 MHz / K. At the 40m, we actually see more like 110 MHz / K at DC.
Assuming that you will always have 3 deg p-p fluctuations down there, we need a gain of 60 at 24 hours. This means that the UGF should be ~24 hours / 60 = 20 minutes. So that sets the maximum amount of foam that we are allowed to have on the can.
That ought to allow us to make the measurement for the first phase (the one with the double AOM setup).
For the second stage, we ought to use your Aluminum box idea. Put a 2 mm thick Al box completely enclosing the RC can leaving 4-5 inches of space. Layer the outside of the Al box with a 2-3 cm thick sheet of foam to keep the heating power low. In that setup, we ought to be able to go wild with the RC foam since the DC control will all be done with the faster Aluminum heater.