Thanks for sharing your adventure. Just a few quick comments:
Garmin provides detailed instructions on setting up the G3X autopilot. See the G3X Touch Installation Manual. The changes I have made on my FX-3 are to reduce the authority of the pitch and roll servos and reduce the roll gain. However, I think it's unrealistic to expect a low wing loading and slow Carbon Cub to behave like a Cirrus when on AP in thermal conditions.
When flying in strong thermal conditions use the airmass, don't fight it. It can save you a lot of fuel on a cross country flight. That requires manual flying. The longest trip I made in my FX-3 was Yakima, WA to Phoenix, AZ, in June. Hand flown working the thermals most of the way.
I have never flown the 340 Titan engine but I have seen other reports of overheating. I don't know what the CHD mechanics showed you but the only way I know to richen WOT mixture is to increase the size of the main jet.
If you made the flight in the last month then Arizona wasn't hot. Try it in the summer.
