OK, just be aware a different setup may be cheaper than making something to suit what you have!
A conventional thyristor or triac will only turn off again if the
load current (not gate current) is interrupted externally; eg. they are great on AC supplies, where the supply reverses through zero, but useless on DC.
(A BTA08 is also only rated 8A, you need something rated well above 100A to suit the motor).
You would need a large power FET (or several in parallel) or possibly a large IGBT. The current rating should ideally be well above the maximum possible motor current.
If you want to reverse it electronically, you need four in "full bridge" configuration.
These look to be a reasonable rating?
Each device needs a high current gate driver; eg. you could use half of one of these for a single device, or two for a full bridge, though using two in parallel may be needed for such large devices - the one above has a gate capacitance of 7nF, so needs a lot of current to switch quickly; a 3A driver is really the minimum.
You also need a current sense circuit to restrict the PWM duty cycle or kill the gate drive signals if too much current is drawn, to protect everything.
A hall effect current transducer such as this may be appropriate:
If you trace back the gate drive circuit in the controller you have, you may be able to a find logic-level PWM signal / signals that can be used to control the new gate drivers?
Start off with a tiny 24V motor while testing things out, and ensure the current limit part works properly, as a fault in the drive circuit or control waveform could otherwise the FETs and/or batteries etc. before you have time to realise anything is wrong..
(There is an old saying about transistors being created to protect fuses - no standard fuse will help a transistor under fault conditions. There are semiconductor fuses available, but 100A+ ones start at around £25 [plus a holder], more expensive than the power FET!)