So you think there's no way I could get an IR receiver that draws 0.35mA to draw less and still work?
You can hardly get it afaik, but you may design such. I am currently coping with the same issue, the standard TSOP1738 from my junk box takes ~1mA. Thinking about a low power IR "detector" (few uAmps draw, detecting 38kHz infra signal), which wakes up the mcu and the mcu then switches on the 1738.