This works: Use a prepaid gift card (like a Visa) to order the bloods through PrivateMD and just enter a bullshit address in the closest state that allows it when you check out. Google the address of the nearest McDonald's to the clinic you'll get bloods done at in say CT, and use it as your address to check out with on the site using the gift card. Then when you get to the clinic, in the off chance they ask for ID, just flash them your credit card with your name on it or even your driver's license, they don't really give a shit what state you live in.
If you have a passport, show them that if they ask for ID. It doesn't have an address on it, only a place of birth.
Another option I've proposed to some of my NY friends and have heard that it works, depending on your bank, is use your own credit/debit card. When you go to check out on the site, enter all info correctly as you normally would, just change the state to the state you're having the bloods done in. So enter your own address and zip code, but just change the state, and most banks never stop the transaction since the zip code matches.
It's gonna cost you an hour and a half drive to get the tests done, but you could always move to Texas bro. There's plenty of room, The 44 might even put you up in his guest bedroom until you find a place....