Someone armed with enough VC money could possibly do that on a really large scale and even monetize it via carbon offset certs and then just throw the C rich output of their giant bioreactor into the bottomless pit.
You calculate the cost of manufacturing hydrogen from water to feed into a the Haber-Bosch process to produce ammonia. All you are doing is replacing the existing steam reformer with an electrolysis plant.
But the what if is what if you can take a further step and directly create amino acids instead of ammonia. You go why do that. The answer is an acre of solar panels produces 25-50 times more energy than corn.
This. It's widely underappreciated how much more efficient solar panels are than plants at harvesting sunlight.
Forget amino acids, those are hard; if we could even just create sugar directly from electrical energy we could save a shit ton of corn being grown and turned into HFCS.
Off the top of my head, for a given amount of wood biomass, you can get about a 70% ratio of product to fuel if you use a high-efficiency wood fire to cook the wood itself.
Then you can take that carbon, bury it in decommissioned open pit mines, or use it as a soil additive (biochar), where it will sequester the carbon for thousands of years and act as a fertilizer.
You could also pair the biochar with a fast-growing swamp tree (willow?), re-incorporating the char into the areas around the willow plantation to create a sort of artificial peat bog which could also be useful for water storage and filtration.