You could get a second output shaft setup for staton's gearbox, (you can upgrade the existing gearbox, I believe, with a new cover and internal shaft. Check with Staton - he refers to this as his
'Tri-Hybrid' gearbox.) Then use the new output shaft to drive a small permanent magnet (PM) dc motor, operated as a generator. The gearing between output shaft and motor shaft should be set so as to provide max PM motor RPM at max engine RPM. The middle shaft on Staton's gearbox spins at about 1600 RPM with an input of 7800 RPM (Max for the GX35) so if your generator has a max RPM of 4200, you would need a 2.6 to 1 speed increase.
The two photos below are from Staton's site; the second photo shows an electric drive motor (250 watts or greater) which could be used to push the bike in addition to, or instead of, the gas motor. What I'm suggesting is that you use this shaft and smaller motor strictly as a generator. (If you do go with this approach, get the smaller, 1/2 inch shaft, as it will be easier to find small sprockets/pulleys in a smaller shaft size.)
Depending on the 'generator' speed, it
might be better to extend the primary shaft on the gearbox, instead of using the middle shaft. This means that the aux. shaft would be driven directly at 7800 RPM max, rather than the apx. 1600 RPM of the mid-shaft. This means that for a 4300 RPM generator, you would reduce the speed by 1.8:1, instead of increasing speed by 2.6:1. However, you would probably need to use a belt (A 1/4 inch V-Belt or a 5mm synchronous belt instead of a #25 chain, as driving a chain directly at 7800 RPM may cause problems. At the lower RPMs at the mid-shaft, you could drive a chain directly...)
Most small DC motors operate in the 3000 to 10000 RPM range. Your motor should have a rated power near the output you're looking for, at as close to the output shaft RPM as possible. A 1/25th HP motor would easily provide 20-30 watts of electrical power.
The motor should be totally enclosed (if not, you'll have to provide a weather-resistant shroud for it,) and be rated for continuous duty. You will need a regulator between generator and battery/load, and if at all possible it should be a switching-type regulator. (linear regulators waste too much power.)
You might want to look at a nominal 24/28V motor (at full speed of your engine,) and add a small solar power battery charge controller as the regulator.
This motor, at Surplus Sales, might be just the ticket. (Solar charge regulators are efficient, they allow input voltages over a wide range (as "12V" solar panels can put out up to 30 volts) , and they have the lead-acid battery charger circuitry built-in. I've seen
some that are in the 15 dollar range, for a 60 watt controller.) And, the wiring is extremely simple for these things... see below.
Another advantage in using a 24V motor, with a switching-type regulator (or solar charge regulator,) is that the engine RPM wouldn't have to be at near maximum RPMs for you to be producing enough voltage to charge the battery - the solar regulator allows voltage between 11 volts and 30 volts to go to the load and/or be charging the battery. So, you can charge over half the RPM range of the engine.