The major source of pain for you seems to be your mash step, there are 2 simple ways to address this:
Go BIAB , and insulate your kettle with an old sleeping bag (or similar) to address the temperature stability issue. The bag should act as your filter, and allow you to remove the grains without having to transfer to another vessel.
Convert a cooler, and add another vessel to your process. You could still bring the BIAB to this solution, using it as your grain filter, and simplifying your clean up process (simply raise the bag, allow it to drain, then dump the grain).