Small scale gas-to-liquids via Fischer–Tropsch — is it even possible?
It probably isn't practical to do Fischer-Tropsch on a small scale
Gasification of biomass is easy. And produces syngas, a mixture of carbon dioxide, carbon monoxide, hydrogen and other compounds.
But the Fischer-Tropsch process to convert that mixture into useful liquids (like diesel) is not easy. The process requires carefully designed reactors, controlled heat and specific catalysts which are poisoned by many of the typical minor constituents of biomass originated syngas (especially any containing sulfur). So industrial reactors have to clean the syngas so the catalysts are not poisoned.
It is unlikely that you will be able to build a carefully controlled reactor that guarantees the right conditions (moderate but controlled temperature and pressure, complex geometry, specific catalysts, clean syngas). Even less likely that the result will be remotely economical on a small scale given the required cost and energy consumption. Heck, major chemical and oil firms have been trying for decades and few of their efforts have been  economically viable.
And there is another reason why this is futile on a small scale. Syngas itself is a usable fuel without further processing. It has been used to power engines (when diesel or petrol/gasoline are scarce as they were during WW2). And variants of syngas were once common as a piped domestic fuel for heating and cooking (before natural gas which is mainly methane became far cheaper and less toxic for most customers). So why not just burn the syngas?