This objective is extremely difficult because of cost. Our atmosphere is huge at technological scale.
The hard point IS the method to do it. So my feeling about "I want to crowdsource, but how to absorb the CO2?" is less than enthusiastic. I'd be far more pleased with "Here's how I want to absorb the CO2 economically, you can check the provided figures including cost" - and then, funding details wouldn't be a problem.
Presently, the most advanced projects don't extract CO2 from the atmosphere, despite we'll have to do it. They only catch the CO2 at a few sites that produce it, locally and in big amount. Power plants, cement plants. Already this is badly difficult to pay, and the efforts collapsed after 2008 when the price of CO2 emission rights dropped.
Besides compressing gaseous CO2 in some natural reservoirs like abandoned gas and oil wells, a tried approach uses silicates. These don't release CO2 to produce, as opposed to CaO for instance. Added CO2 transforms them to silica and solid carbonates. The silicates aren't processed, nor even moved: CO2 is injected in the ground at the silicates.
These two attempts cost magnitudes less than scrubbing the CO2 from the atmosphere with a processed chemical, and nevertheless they find no use because of cost. So I suggest to put some cost figures early on any attempt, even if the detailed compounds aren't still known. Do you plan to move air actively for instance? Even power plants don't do it at the cooling tower.
Grow bamboo to bury it, deep enough that most carbon stays there? If you catch the methane it has a value and is emission-free. Or collect algae without growing them? Collect wood waste when a forest is harvested? At a paper factory? Vegetable waste on crop fields? At the bottom of a barrage lake?