Has Back EMF Coil collapse spikes been used in a BEAM solaroller?

Actually, I know nothing about BEAM solarollers. Is the lighting at a point where it is impossible to have continuous operation of the motor? Does it have to move in fits and starts? Because if you can keep the motor running, that would be best. And if you do, there won't be any back EMF. Back EMF requires that the motor acts as a generator. Which means you aren't driving the motor but instead allowing excess field energy you've already supplied to return (which is never an efficient process.) You'd be better off supplying energy in a fashion that is 'just right' so that you aren't faced with losses involved in recovering excesses. All of the energy should, at best, be converted to frictional losses in the end, not back EMF you have to recover.

You'd have to stop driving the motor for a period of time to get a back EMF. But there is capacitance in the motor and that will waste part of the energy as it reverses polarity (you don't get to recover that part) and some of the rest will be lost in resistance as well as your recovery circuit as the motor finally returns some of that energy as it comes to a stop and acts as a generator (more wastage in the stopping process and having to overcome stiction again.)

It just doesn't make good sense to me. Not for something depending entirely on a tiny solar cell in a competition.

And keep in mind, in your amazement at the "100's of volts" possibility you also need to be aware that 100's of volts is not power*time or energy. It's volts, which is only part of the equation. You need to know current, as well. And for how long. "100's of volts" occurs when it's driving a very high resistance load -- inductors will generate whatever voltage is required to allow the current to continue on a declining slope, starting from the current you left off at when you stopped driving the motor. Anyway, this isn't the way to do things.

Cars, on the other hand, do have to obey traffic lights and traffic, so people use braking a lot. In those cases, where sudden or frequent intentional stopping is the order of the day, then it makes some sense to try and recover some of that since stopping is a requirement of the application (driving.) But on this kind of thing?? Why would you stop???

This argument assumes that you can drive the motor continuously, efficiently. If overdriving, then stopping again, is the only way to achieve efficiency.. then the argument becomes far more nuanced and... well, then I don't know.

Yes .such a method has been used .The BEMF of the collapsing field is used to recharge a battery or a capacitor.There are many circuits online for this mostly by fringe scientists and alternative energy buffs.

I'm not sure on this but I think all you have to do is put a secondary coil next to the coil from which you want to extract BEMF.This secondary is dioded so that when current is supplied to the primary,no current is induced into the secondary.However,when the BEMF occurs the secondary will capture that voltage.