what in the sam hill do these do? Power stacks?

When the exhaust valve just opens there is still about 100PSI in the cylinder. This roars past the exhaust valve at supersonic speed. Although we do not normally feel it, air has mass as does the exhaust. That mass and velocity creates inertia as that slug of exhaust roars down the exhaust pipe. When the exhaust valve closes, this creates a low or negative pressure in the exhaust. I assume these had a check valve in them to prevent exhaust getting out.
The early emissions cars had air injection pumps and a passage in the head or tappings in the exhaust at each port. The carbs were jetted rich to provide unburned hot fuel that just needed more air to burn again in the manifold. Then they went to a gulp valve system with a check valve. When the exhaust pressure went negative the check valve opened and let in a bit of air. No expensive and bulky air pump.

If the stacks did indeed have a check valve, that explains a lot.