The problem is you keep reapplying the jailbreak, when you do that you are undoubtedly going to mess up the filesystem. Jailbreak once, that's it. If the device doesn't boot use just boot, do not rejailbreak it.
You only need to worry about preserving baseband once you get to 05.13.04. 06.15.00 is automatically preserved because iTunes recognizes it as the newest baseband.
Restore iOS 6.1 again. Run Redsn0w to jailbreak/hacktivate. Then run Redsn0w again and downgrade baseband. Now boot tethered with Redsn0w, open Cydia and install Ultrans0w and Evasi0n untether and you're done.
Every time you run Redsn0w you HAVE to be in DFU mode, if you are on the springboard it will not work.