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Just to clarify. Microwaves do not penetrate from the inside out. The energy comes into contact with the outside surface first.
Aluminum blocks electromagnetic waves. The bottom of the case is foam rubber. That's the entrance point.
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The IR TX should be modulated and an IR RX module should be used. This will take care of sunlight / heat issues.
You can also use a direct switching replacement for the 7805. It is the "oki-78sr series" of switching regulators. I have used them and they do cost a bit more but work well.
Well... the joule theifs output is switched as well. Not steady state. But, you could try replacing the Ni-Cd battery with the super cap.May work great and might have to give it a try.