So I got some time this weekend to implement my plan of using FDA silicone caulk to glue stainless foil to the bottom of FDA silicone sheet. It flexes well enough to fit inside my keggle.
I used an SS Brewtech recirc manifold to get wort return through the middle and provide some stability for the cap so it doesn't bend downward. The manifold is a little larger than my keggle opening but I can angle it in easily enough. I was worried that the manifold would be too heavy and sink the whole cap but it stays afloat. The recirculation even pushes up on the cap to prevent it from breaking surface tension on the sides.
My only issue was with the stainless steel foil. It was difficult to bend up to make a bowl shape, and is very sharp. It cut my hands up tring to get it in and out of the keggle. Thinking about just cutting it flush so it doesn't have the lip, and putting some silicone tubing around the sides so it doesn't cut my hands.