LPG conversion requires a lot less changes though. The gearbox and braking remain exactly the same. You need to make very few changes to the motor. Then you just add a little more equipment (fuel tank, computer and control system) on top.

The brakes would be the same, and you're just removing-not replacing-the gearbox.

For front-wheel-drive cars (which about 95% of small cars are), the differential is embedded in the gearbox.

So you can't remove the gearbox, or you'll have to place a new stand-alone differential, which will add significant costs.

Just make a shaft to replace the shifty gear reducing bits of the transmission and then bolt your electric motor to the now gear-less transmission. It should be pretty easy to standardize a coupling and mounting bolt pattern for the motor and then just bolt on whatever transmissions shaft and bell-housing adapter you'd need for the particular model.

I'm glossing over the details but you'd need about half a dozen precision machined features and like three or four parts that are specific to a particular ICE engine/transmission application. Dimensions are such that you could probably buy cheap axles for a common application and then have them machined down to make your part. Parts cost should wind up under $200ea unless you need something expensive to machine (like blind female splines).

Where are you going to get vacuum from, to power the brake booster?

An electric motor, you'll need something to run the power steering pump too.