Factory unlocked means baseband is of no concern to you. There should be no problems associated with your baseband.
As stated before, baseband cannot be downgraded. Once you go to iPad baseband there is no going back. The only way to change would be if Apple issued a baseband higher than 6.15. When you jailbreak again, select flash the iPad baseband and deselect install Cydia.
There is an option to go to the iPad baseband in redsn0w. It comes up once you start the jailbreak process. REMEMBER THAT YOU WILL LOSE GPS!! And no matter how many times you ask here, you will not be able to fix that. However, your phone will be able to use cell tower triangulation, which is less accurate than GPS, and very inaccurate outside of cities.
Your phone is safe to go to the 6.15 baseband, but remember that you will lose GPS permanently. You can downgrade to any iOS that you have hashes saved for. However, that does not affect the baseband, which cannot be downgraded, only upgraded.
If the phone is not too new, you can go to the iPad 6.15 baseband to unlock. Let us know the 3-5 digits of your serial number before doing this. Also, you will permanently lose your GPS function.
Baseband cannot be downgraded. Using the restore button in iTunes is what got you into this mess. Your only option to restore an unlock is to go to the iPad baseband. However, you will destroy your phone if it was built in the second half of 2011. Also, no matter when your phone was built, you will permanently lose GPS.
You must supply the first 5 digits of your serial number first, in order to know if this can be done.
Baseband does not affect jailbreak.
No, that's my bad, I didn't know you were on the official carrier. Ultrasn0w is unnecessary.
You still have to have ultrasn0w. SAM is an activation tool not an unlock tool.