if power cycle fixes the problem it's not likely a part in the sense that it's not a sensor or plug etc.
What you just described is an electronic overheating situation.
The 3.0 doesn't have a fan in the eBox. I'm willing to bet that if you added one your problem will go away.
The trick is trying to reproduce the problem which requires a long hot drive however:
If weather permits (zero chance of rain). Remove the top of the eBox to allow some airflow for cooling.
I'm not sure what reset happens to get something to recalibrate but there are a couple known bugs in the DME including one with the engine core temp that could throw things into disarray.
If there is enough room in the eBox you could put a heatsink inside and outside and the heat can conduct though the screws (use fat aluminum screws).
Not sure why the V8 get eBox cooking not the i6.
Good q on the ccv. Pull the oil fill at idle it should stumble a bit. If it gives you PTSD look for a leaky hose in the ccv or blockage.
Also goes without saying but check all the intake for leaks. Spray butane from unlit torch (maybe even lighter is enough) and watch for rich feedback on O2 sensors.
The hardest part will be trying to reproduce it but if it's hot eBox related open the hood and park with sun on the box. In FLA that should simulate 2 hours of driving in about 10-20 minutes.
Drill a small hole and put a stick thermometer in there to monitor temp.
Most Electronics don't like temps over about 160F.
My theory is you heat up the engine and engine bay from a solid drive that will heat soak the firewall and chassis. Then when you stop to eat, that heat soak comes out and with no moving air you get a temperature spike that makes something electronic go haywire.
I would get some baseline temp inside eBox and then loosen the cap to allow some air flow or even remove it and see if you can 1) reproduce the problem just using sun as a heat source to save needing to drive a couple hours. 2) cool the eBox to see if the problem will go away.
I have read of similar problem with V8 e53 and eBox fan failure what made me think of it. If I'm wrong and 3.0 does have a fan than make sure the fan is working.
I'm not always right but it rounds. Heat won't affect an O2 sensor but it will affect what it's plugged into.
Swap your banks. You should eventually get some error for mismatched bank one/two but with any luck you'll get a repeat of the O2 error you have been getting but on the SAME bank = opposite sensor. That means the problem is in the wiring or the DME.
If I recall correctly the DME is only screwed together you can open up and look for cold solder joints etc also get some deoxit pro gold and treat all the connections in the eBox.
Get the pure stuff with high reviews on Amazon. 5-10ml is a lifetime supply for most people but not the diluted stuff.
Just checked via parts supplier and if 3.0 had a fan it's a different one. I would look into some cooling solution for the eBox but at least you can do some testing to confirm if eBox overheating is your problem.