Just something to try maybe...
Assuming you have an overflow container installed, you might want to try a 4 lb. radiator cap until it STARTS to overheat again. When it starts to overheat, you should be able to see the condition of the coolant that's coming out into the overflow. Look for bubbles, discoloration, etc. With the low pressure cap, you should be able to CAREFULLY remove the cap to see if it's circulating also. I don't normally recommend it, but you've obviously got something strange going on here.