II don't think making a fake TSDZ2 would be worth the effort, I doubt such a thing exists. You've likely got the non-throttle version. Yes you can upgrade it but that involves a little soldering. See here for the pinout: https://github.com/OpenSource-EBike-firmware/TSDZ2_wiki/wiki/Wire-KT-LCD3-to-TSDZ2
Then look here for how to solder on wires for the throttle: https://github.com/OpenSource-EBike-firmware/TSDZ2_wiki/wiki/How-to-install-motor-temperature-sensor
These instructions are for installing a temperature sensor, but it uses the same output on the PCB as the throttle, so you solder the same spot. Just look at the labels in the 6 wire image.