When you cleaned the battery cables, you could have easily reset the computer to factory settings. However, the negative battery cable on mine corrodes like a mother. So replacement is probably the best idea like you are going to do.
Yeah like you're saying the kit and such is def a start and can be done yourself too which is nice on the wallet lol. Just make sure to take your TIME if you do decide to do all of that work yourself. Transmissions are super finicky as you have come realize. Proper torque procedures, alignment, etc are all important. I say go for it man!
-2011 F-150 Lariat: 5.0 "Coyote" V8, 6-spd Auto (6R80E), 3.73 ELocker. White Platinum Metallic Tri-coat.
-1992 Ford Ranger: 4.0L OHV, 5spd (M5OD-R1), 3.27 Open.