I tried to get some specs on the engine but I didn't see if it was a single cylinder or a twin cylinder. I have used both and the twin cylinder has a more steady air input which makes it easier to control with an air control box we call the Electronic Carburetor. It takes an O2 sensor and uses the signal to control an air inlet valve that keeps the air fuel ratio dialed in a tight working range. I made a step by step book on the process, here is a video that explains more:
For that engine the load control would be handled by the generac electronic speed control governor. It will take care of itself. You would get roughly 3.5 - 4 kilowatts of output on that generator with woodgas. There is some nitrogen in the gas that makes it less potent than propane, but still good.
Your build could work fine I think, but it is probably as small as I would go in engine size. Small engine don't pull as much air inside to break down the wood, so you compensate with smaller 1" branch rounds or cubes. Softwoods would be preferred during operation. There is a chart in my book that tells you exactly what dimensions to use in the hearth.
I like generac stuff. Can't go wrong with propane.