To break it down:
- you need something to spin the transmission for motion (new electric motor).
- you need something to spin the hydraulic pump (looks like 2 section pump) for FEL/backhoe and steering.
I'd mount the new electric motor to the transmission stub with any necessary gearing (if any) and put a gear on that shaft to drive a chain to drive the hydraulic pump off to the side.
The motor will have to run continuously to provide power to the FEL/backhoe and steering, and will only be tasked with running the transmission when it's moving.
However, by using only one electric motor, you'll have some parasitic battery drain because of spinning the transmission even when it's in neutral. So maybe a separate electric motor for the hydraulic pump(s) would be better.
You won't need that complicated of a drive for the electric drive motor. Maybe steal something off of an electric forklift salvage.
Interesting project. Many considerations. Good luck.