Here's what needs to happen... since you're using the 6.15.00 iPad baseband, you'll need to create a custom IPSW (iOS Firmware File) that you'll use to restore to via iTunes. The only problem is I'm not 100% sure if redsn0w (the program you'll use to create the custom IPSW) supports iOS 6.1 yet.
Give us a little time and I'll get another member of our staff to check in here and help us out.
I don't believe that there's support for anything above iOS 6.0 at the moment, I don't have the blobs to verify this at the moment. Although iOS 6.1 is a hotfix for iOS 6.0, it's not entirely supported since all iOS 6.0-6.1 jailbreaks are using the iOS 6.0 IPSW. But instead of creating a custom IPSW, you can try using the Restore feature in RedSn0w > Extras > Even More > Restore. This feature already incorporates a "preserve baseband" protocol. After selecting the IPSW and your blobs, there will be 2-3 windows that pop up, one asking are you sure that you want to do this since it'll wipe your device, the second being do you want to upgrade your baseband and such. Answer them accordingly to what you want and it'll do the job.
Alternatively, you can downgrade your flashed iPad Baseband using RedSn0w, do a manual restore, rejailbreak/flash it and reunlock it with UltraSn0w. Make sure that you install the UltraSn0w Fixer for iOS 6 (included in the UltraSn0w repository) so that it runs on your 3GS.