Update on my issues - I was trying to avoid adding a second battery to my boat, which is what this circuit will require. Adding the relay will not stop the starter motor from drawing down the battery voltage, assuming everything else is the same. I am going to try this circuit with a single battery first, but I am not expecting any better results than I already have.
I finished cleaning up the ground on my existing battery - replaced the crimped-on 2 ga connector with a clean bolt-on battery terminal connector, and ran a clean 10ga ground from the battery negative screwpost to the dash (I tied it to the existing ground behind the dash, Y'ing in the 2 PP ground wires at the same time to ensure I had the best possible ground for the PP). Net results: No better behavior - the PP still resets every time i start the engine, as does my radio.
I will try this circuit next weekend - i have the relay in hand.