How do I unlock my iPad2 after downgrading from 6.1.2 to 5.1.1?

I recently purchased an iPad 2 at 6.1.2. Fortunately, the previous owner saved the hashes for 4.3.5, 5.1.1, 6.1.2 et al. in between. Using the procedure in a tutorial elsewhere on this site, I was able to successfully downgrade from 6.1.2 to 5.1.1 using Redsn0w and then Jailbreak with Absinthe. So far so good. I would like to switch to T-Mobile but it appears that the iPad2 managed to get relocked to AT&T. Yes, I know that they are all supposed to be unlocked. When I put the T-Mobile sim in the device, it still indicates AT&T 12.0 as the carrier even after a reboot (T-Mobile guy said it sometimes gets relocked during a restore in iTunes). I called AT&T to get it re-unlocked and they said that they reissued the network unlock and that I should backup and "restore" my iPad. Option-clicking the "restore" pulldown in iTunes tells me that it will erase and reinstall 5.1.1. Since I'll be using a locally stored IPSW (from iClarified) and Apple isn't signing 5.1.1 anymore how will it know to unlock the iPad? Furthermore, it takes an hour or 2 (or 3) to reinstall the OS, sync, Jailbreak, add all the Cydia apps etc. so I don't want to do this capriciously. Is this correct? Will the IMEI unlock be restored if I go through this entire process again? I'm now completely confused!