The belt from the motor goes to the clutch so if the motors on it just spins ant the clutch. when the clutch is activated it moves the belt to the wheel.
So what you're saying is.... It's a solenoid which pulls the small gear in towards the larger gear?
Hhmm... It's really hard to offer suggestions without having the assembly in my grubby hands.
Might be some way to permanently set the solenoid in the "closed" position. Like a place for a cobble pin or adjust the small gear accordingly. You might even be able to Macgyver it a bit with a suitable washer and a carefully placed blob of solder. That might ruin the solenoid if you ever desire to reverse the modifications or the solder might not be strong to hold to the abuse. Maybe one of those locking collars with a drop of loc-tite instead of solder? Would be a PITA to find a fitting collar though. Might find something that would fit in a well equipped store that sells steel cable.
Another way, but it might be a little more work, would be to see if you can adjust the big main gear on the steering wheel along the shaft so the teeth fall in line with the belt between motor and clutch. Can't tell if the bolts would get in the way of this though. If you can do that, then you might be able to remove the large belt and use the belt for the clutch/steering instead, bypassing the clutch entirely. The motor looks like you can adjust tension on the belt and there might be enough play there to get the right tension on the small belt. The immediate problem that I can see is that you've effectively doubled the speed of the motor by bypassing the reduction gears of the clutch.
I'm kind of running out of suggestions that don't require fabricating whole new asssemblies.
I'll chew it over a little while longer.
Is it possible to snap a photo of the clutch in the engaged position? I think I know what it does, but I just want to be certain.