Re: biochar -- If you have access to water to put out the fire, the easiest fastest way to make a whole lot of biochar is just in a pile on flat ground. Start a small fire, when the coals start to turn white put on another layer of wood, repeat until you're either out of wood or the pile of coals gets too big to work safely around. Hose it out good while raking it back and forth, but don't breath the steam because it contains carbon monoxide. Usually for me by the time it's too big / too hot I've got a pile that's like 10-12 feet in diameter and 2 feet high in the middle. The next day after it has cooled off, I drive back and forth over it with the truck to crush it into fine particles. As others have pointed out, to reduce the alkalizing effect of the charcoal, you're gonna wanna mix it with compost and let it sit for a few months or a year before you disperse it on the land.
With the tree spacing you've mentioned two concerns, soil moisture and fire danger. If you can adopt a management practice where you grow as much vegetation as you can during the wet times, and then trim it back, graze it off, or do controlled burns before the fire season, you might be able to both increase the water holding capacity of the soil while also reducing the fire risk. Growing trees and other perennials is probably the best way to get organic matter down deep in the soil, which increases the soil water holding capacity. Then cutting/grazing/burning the above ground vegetation causes roots to die below ground, which then decomposes into water holding organic material. If you can cycle the vegetation on an annual schedule you'll probably have pretty good results on both fronts, and increasing the soil water holding capacity a little bit every year eventually you'll begin to have an effect on the aquifer recharge.
If it's gonna take 10 hours a day for months on end to get thinned out to a more reasonable tree spacing, you might post on craigslist or facebook marketplace for some u-cut firewood. Flag the trees you want cut or drop them yourself and then let the firewood getters saw them up and haul them off. You never know, you might find a great sawyer who's good at felling trees and might pay you a little bit so that he can turn it around and sell firewood for $300 a cord or whatever.