Yeah, that's the problem - all the Sterling engine solutions end up as expensive, exotic, low production natural gas powered devices. Which means that you need a supply of natural gas, and at that point you have other generation options. There was a slightly lower-power, but much more compact and finished Australian product along the same lines a decade or so ago called the WhisperGen which was intended to replace a hot water and heating boiler. They ended up going out of business unfortunately.
Not sure where you're getting the nat-gas-fired idea from. The more-commercial link I provided seems available as a micro-CHP setup, with a wood-pellet furnace. The Melvin Package from Selfton Motors has a combined propane/wood fire box, but the Melvin engine itself is a separate part, allowing use of a custom heat source.
I'm not sure though why you want to burn wood on that scale. It's really expensive to properly filter the exhaust from a wood stove, and economy of scale doesn't hit in the kW range. I mean, yes, if you're in the middle of nowhere, sure, but I'd claim that an install cost of 3~4$/W(electric) for the Melvin Package, including shipping (even to a potentially-remote location, only 100kg for the largest piece allows transport with e.g. a paramotor or two humans, with additional trips for the cooling jacket/firebox/vents/piping) is acceptable for a reliable wood-fueled electricity source.
Why not a Stirling engine?