Hehehe i am pretty sure they are aware of the fact that there are no other solutions out there so they decide that 300 dollars is a fair price for an equipment that copies the EDID of ur AVR/TV and injects it back to ur HTPC.
I think you are better of spending most of your money on speakers however, as that's what makes the most difference.
So, in my case it could be that the NUC itself is doing a good job or the fact that it runs 24/7 and there are no wake up issuesMost brands of avr have issues with htpcs, and usually it's related to the htpc more than the avr.
should I leave the tv turned on or should I turn it off?Aspik try to turn off your AVR while your HTPC is on, wait couple of seconds and turn it on again. Do that like 5 times in a row and report here your findings.