Two words : " Rocket stove "
Google it for information, or check out Kartographer's stove
Maximum heat from a minimal fuel source
Yes Rocket stove would work, but even then how long do you think it would take not to just boil water, but to actually distill it? Boiling water does kill the biologicals, but what about other contaminates, like lead or the cooper salts from pool water? I would imagine some petrolum and chemical slovents, might even evaporate and pass through the distilling process.
Rocket stoves are good but not really very effective for the volume you would have to boil for water. It would cut down on volume of wood but you’ll still be stuck there monitoring and feeding it.
A gravity filter is easy, you fill the top and go do something else while it works.