I cover my small HFGH with a shade over and leave the vents only open a few inches. I've about taken all the plants out of it for the summer. I'll wash it inside and out with Palmolive soap before covering it to protect the polycarb. When storms are due I shut the vents and door.

An 80% shade cloth cover, to not only reduce the heat load but also extend the life of your polycarbonate, would probably be less expensive than running electrical exhaust fans all summer. Leave the door open unless there are storms coming. Removing and later reinstalling the poly panels could cause problems with the fittings over time.

I'm in SE Virginia (Williamsburg). Last summer I left the doors open and had a shade cloth over my 10x12 (I think it's 70%). Even with the exhaust fan and intake running it would still get hot sometimes. I've added a circulating fan at about the 7' level on a shelf which feels like it's making a difference. For a change, I'm growing 3 rows of corn on the South side of the GH to provide shade at the height of summer.