I've been running more diagnostic tests to prove to myself I'm not crazy and this EVSE plus car won't charge at maximum, "H", level.
I confirmed problem still exists on getting it home. Won't charge on H, charges inconsistently at M, and usually only charges reliably at lowest, "L", level with the Kia supplied EVSE cable. Even though the service department duplicated the failure to charge without shutting down at H with my cable and a 2nd cable, but apparently at least once did charge at H with a 3rd cable, they returned the car with the original EVSE cable at seem to think it's "OK".
I did some detailed tests, I'll talk about in a minute, but after confirming problem still exists, I opened up a complaint directly with KIA Corporate Customer Relations, along with the details of my interactions with the service department and a copy of their report showing they could duplicate the problem at their shop, but did nothing.
First, I was wrong about my dedicated 20A jacuzzi circuit. I thought I had it wired with 10 gauge wire, but it's actually 8 gauge solid copper wire. Cost me over a $100 extra at the time, but I didn't want power problems down the line. Anyway, I opened the junction box where this wire run comes through the wall and attached a clamp ammeter on the line. I then ran the jacuzzi, first on low and then oh high jets with bubbles, etc all going. At low it draws 10.3A and at high the maximum it showed was 20.1A, but consistently above 19.8A and the voltage was still ~ 118V with this load. Only twice in ~ 5 years can I remember this tripping that 20A breaker and upon resetting it, it would then run for the rest of at least another 20 minutes on high. So, this line, with nothing else on it should have no problems with a 12A EVSE load.
I disconnected the jacuzzi and plugged a 10 foot 10 gauge extension cord in so I could reach the car in the driveway. Unfortunate that I had to use it, but this is a much heavier gauge wire than in the actual EVSE cable, and an electrical calculator indicates it should drop the voltage less than 0.3% with a 12A load. I set the car to accept maximum charge rate, H, with a 110V source. I then plugged the EVSE into the extension cord and set it to L level before plugging the EVSE into the car. (The EVSE resets to H level every time it's plugged in to a 110-120V source.) Once the car started charging, I read the clamp ammeter for the real current draw through the entire circuit. I then stopped the charging, unplugged the EVSE from the car and reset the EVSE to M level charging. I plugged it back in to the car and once charging started again, I read the ammeter. I then repeated this exercise at EVSE set to H charging level, and this time left it to continue charging after reading the ammeter. Watching it, I saw the car indicator on the top of the dash go from green to red in about 10 minutes into the charging and then the charging stopped and the light went out. As before the car's NAV screen says "Charger Error" when I first start it up after this event. So, for those of you interested, here's the current draw with supplied Level 1 EVSE cable. Your's may deviate, but probably by not more than 0.3A unit-unit and the numbers below are the maximum I saw with the ammeter showing fluctuations of about 0.1 to as much as 0.20 amps below these max values.
L Level = 7.3A
M Level = 9.25A
H Level = 11.55-11.60A
I can't see any reason a circuit capable of supplying 20A continuously for an hour at a time shouldn't be able to handle an 11.6A EVSE draw. This doesn't prove it's the EVSE and not the car having a problem, but it sure says one or the other is not right. I'll see what KIA Corporate Customer Relations says. Hopefully soon. And meanwhile, we'll keep charging at L or M every few days.