Regarding compressed wood gas, that has been much discussed on this site. Yes, it can definitely be done. There is a bit of a question mark yet about how stable it is at high pressure over time, but there is a YouTube video of a fellow who stored gas over part of a winter. Given the low temperatures it may not be a completely fair test (reactivity proportional to temperature), but more or less it demonstrates.
But… Wood gas is not efficiently compressible like butane or propane, which could be likened to mousetrap springs. Also, wood gas has a low calorific value due to nitrogen dilution. So the energy required to compress it represents a significant proportion of the energy of the gas.
So the conclusion is that compressing wood.gas can be done, but is not practical in energy terms, but may serve for special applications, recognizing that the efficiency is practically nil (ie, cutting torches).
Retort gas, as you seem to be aiming for, may be a better candidate, as the gas isn’t diluted, so is more energetic.
My suggestion - aim for the proven “gasometer” technology. Basically a large gas bag, weighted at a few pounds pressure, minimum energy input, maximum functionality. For stationary applications bulk isn’t such a bad thing.