I have been interested in the series-hybrid configuration for some time, but only as a range-extender for an EV, where the trailer is only used on rare occasions.
Gasoline engines are easily converted to run on propane, but I would recommend doubling the cc displacement to roughly get the same power as the appropriately-sized gasoline engine. Concerning sizing the generator...
It depends on what you want to accomplish. As many here know better than I, a motor sized large enough to handle desired accelleration power without any significant heat occurring, would be larger than neccessary during cruise mode, and range would suffer. If we make the motor smaller, so that it gets a little warm on accel, it will cool off during the 90% of the rides "cruise" speed.
Then if we raise the input voltage from the motors constant-duty rating, we can use an even smaller motor, which may have the benefit of being lighter and cheaper. Each bikers use-profile must balance temporary heat build-up against cruise-mode heat-shedding ability.
Adding a gasoline engine to turn a series-hybrid generator (on-board APU, or on a trailer) can be small enough that it only provides range extension, but so small that even if miles are doubled (for rare special trips) the battery pack is still depleted. In this case, I would recommend the gen output watts be equal to the wattage rating of the motor being used.
If you wish to size the series-hybrid gen to provide unlimited miles, you can use a very small battery pack as a "surge tank" to smooth and level demand/output , but the watt rating of the gen should be approximately double the motors wattage.
This is based on an Idaho university series-hybrid experimental Taurus that was run by a motorcycle engine. During accel, the motor drew amps from both the small battery pack/capacitor and the gen. During cruise the motor only used the battery, while the gen recharged the battery and a large capacitor. (I checked the link from my files but its no longer active, its from the early 90's)
If you accellerated frequently with insufficient "battery charging" cruise time (such as in "downtown" city driving), the small battery would gradually be depleted, and you would have to pull over and idle to top-off. This use-profile would require a larger engine/gen and a larger battery pack to achieve uninterrupted use.
At a minimum, a 25cc gasoline engine, or a 50cc converted to propane "should" be more than adequate. I would definitely recommend the 4-stroke for reliability and longevity (no oil/fuel mixing, much better bearings, much cleaner exhaust, and quieter).
If you wish to use the edger motor for the initial experiments, it might be easier to put it on a trailer. A tiny automotive alternator (Geo Metro?) can easily have the voltage regulator hacked to output 52V to feed a 48V battery pack. Free "trash-day" treadmill permanent magnet motors (PMM) typically run off of 90V DC. You could size pulley diameters to have it output 52V...Just a few thoughts....best of luck !
[edit: added link]
http://www.qsl.net/ns8o/welcome.html