CC, thanks for the thorough and clear narrative. That's some good writing. I easily envisioned myself on the bank watching the process.
Here's a thought for topping off a slow leaking pond with ice cover.

I may be all wet; I've never tried this but, since you have a close approximation of the present leak rate for your pond, how about trying to add water with your hose under the ice at a rate equal to or slightly less than the leak rate? The idea would be to not puddle water on top of the ice but to keep in underneath to support the ice cover?

You'd have to figure a way to keep the hose from freezing if it were not running of course-bury it, insulate it, something else? If the discharge were under the ice cover and the rate of flow was slower than the leak, would the additional water buoy the ice cap without running out on top?

Has anyone here tried such a thing? I'll set up the experiment this winter on my pond just to learn. The discharge end may have to be in deep enough water that the warmer water (less dense) mixes with cold water and doesn't rise the top and start melting the ice.