If you're trying to get hired as a team, that sounds new, so employers might not have heard of such a thing.
It's the first time I've heard of something so preposterous. Maybe if it was a progressive state like Colorado, I could understand, but Tennessee? I can't stand the hot, humid summers myself. Then you have chiggers and scorpions to worry about. ;)
Getting hired as a team is hardly new. Acquihire is incredibly common, and this is essentially the same thing.
As to Colorado vs Tennessee: Maybe it's not for you. I personally prefer our city as a well kept secret.
My previous company also was relocating and we wanted to stay as a team. We sent few e-mails to companies that had similar profile. We thought about placing advertisement in national and financial newspaper, but because it was relocation and not lay-offs we were not sure if that would backfire. Few companies hired more than 3 persons each out of it and maybe one had small team afterwards.
You have to be lucky to pull this off.
As for hiring a team, I have heard of companies poaching their competitors' employees before, not as a whole team at once, but one by one (they hire one guy, then he talks to his former co-workers and they switch to the new company too). I'm not sure why companies don't do more of this when they can; it'd be a great way of beating your competitors, since the employees are the ones who build the product and know everything about it. There's likely some non-compete issues in some places, but in California that shouldn't be a problem, as case law already bans enforcement of non-competes, and that lawsuit a few years ago with the big tech companies proved that non-poaching agreements are also illegal.
Edit: The hiring company was in Alabama. The closing company was in the back woods of California (not SV).