Transmission won't shift into 5th, P0605 and P0700 codes

I've got an 07 KJ cherokee 2.8 diesel automatic which showing a check engine light. Ran a diagnostic and the engine control unit has code P0700, TCM showing P0605. Have had it looked at by a couple mechanics who won't touch it due to its age and the fact it is a Jeep (hard to source parts for Jeeps here in south Western Australia). Was recommended a transmission replacement or full rebuild by a specialist, seeing too many dollar signs to jump into that just yet without troubleshooting..

Engine won't shift into 5th gear, and takes off rather slow from a stand-still. Was told that tyre pressure in the rear tyres might be effecting the ABS system to override into 4WD if the PSI drops 5 points below where it should be, so perhaps thats the cause of the slow takeoff. But check engine light is on, won't shift into 5th and engine will start overheating if we take it over 2700RPM, but drops back into reasonable temp when around 2000RPM. Potential thermostat issue as well?

Have also been recommended that the battery health could be causing the ECU to not send proper signals, multimeter on the battery showing 12.37v and should be reading 12.6v or above in order to guarantee its working well, so might have to chuck a new battery in it, try and reset the codes by draining residual power first and starting up with new battery in hopes it sorts it.

Anyone have any experience with this sort of issue? How did you sort it?

Have a look at the cables and connectors around the gearbox, p0605 is a TCM fault, jeeps name for the gearbox controller.
I did some work at Port Headland years ago, beautiful country.