"Wet thermoacoustic" or "rice" Stirling engine with flywheel experiment. Not working (so far).

I've been experimenting for some time with this idea of adding a flywheel to the "rice" engine. Nothing much to show, so far.
I've tried different amounts of weight, different temperatures, different amounts of internal pressure, etc. but nothing has worked so far.
if the flywheel assembly is removed, the engine will run, and appear to run strong.
put the flywheel back on and you can see the results.
I suspect the reason may be too much disparity between the "natural" frequency the engine wants to run "free piston" and the rate at which the flywheel is able to revolve, so the two are working against each other or canceling out.
In other words, the piston/diaphragm is going up when the flywheel is pushing down.

[@thisisajewtube]

I think that there needs to be more empty space under the stack, and that the stack needs bigger gaps (slower heat exchange). Maybe use a partition wall with a separating hole instead of a stack (like lamina flow engine). The membrane also appears thick and hard. And too much water also.

[@peoplesresearchcenter6184]

Probably all good suggestions, but the flywheel apparatus on top of the engine is removable. Just loosen the hose clamp and it can be lifted off.
I had the engine running putting on the flywheel, then after probably an hour of making various changes and adjustments with the flywheel on and not getting it to work, as soon as I took it off, the engine ran just fine again without it. So, I'm inclined to think the problem is not with the engine but with the flywheel attachment.
My guess is that the "lift" distance on my flywheel connecting arm doesn't match with the natural lift height of the diaphragm and/or the rotational speed the flywheel is capable of does not match the engines natural operating "frequency" close enough, so the flywheel is working against the diaphragm motion rather than with it.
The engine seems to run pretty strong without the flywheel. I should have included that in the video, the engine running before and after adding the flywheel.
Of course, any additional improvements to engine performance could improve chances for success.