I'll reiterate the "FHV is no biggie" thing. MOST cats have it or have been exposed to it. And if your vet is giving your cats antibiotics for viral infections, I'd worry about his/her credentials.

Most reasonably healthy cats - including ones with FHV - can fight off the upper respiratory and conjunctivitis with just Lysine-L, and drops or goop (Polysporin Ophthalmic) for their eyes. If your cats get their standard FVRCP shots and boosters, get Lysine-L supplementing (it's super-cheap at the crunchy granola store. Open the capsules and mix the powder in with food), yeah, they might get a little upper resp infection, but it's no bigger a deal than you or me getting a cold. So don't worry too much!

You've been keeping them happy and healthy, and yes, the stress of a move will cause a flare-up. But shove extra Lysine-L into them, feed them well, Polysporin their eyes, and they'll go back to normal in a couple of weeks. I've had dozens of foster cats with URI/herpes/chlamydia, and my own cats rarely get anything more than a little sniffle now and then, if that.