It’s an interesting question.
I think the short answer is ‘no’, there isn’t much pursuit of a medium heating value syngas in the DIY crowd. Excluding the physics issues others have pointed out, chargas is maybe 4 MJ/m3, wood gas is maybe 6 MJ/m3, definitely not worth compressing.
If you could get to 20 MJ/m3 like retort made ‘town gas’ it might be worth it for stationary systems, but probably not for vehicles.
(Natural gas is 36 MJ/m3 for reference.)
It would be possible to do steam gasification at home if you were brave/foolhardy/careful and really wanted that medium value gas.
The Wright-Malta folks built some laboratory scale systems that are well described and appropriate to home experimentation. The context was syngas to methanol but the steam gasification is well documented: