I wonder if, instead of scrubbing CO2, it would make sense to increase the other constituents of air, e.g. oxygen, thereby reducing the effective concentration of CO2. What if we ran a giant hydrolysis operation, generating O2 (and letting H2 escape into space or finding some other use for it other than burning it)?
Second of all, you're talking about gargantuan quantities of oxygen (or nitrogen, or whatever). CO2 is roughly 1/2500 of the atmosphere, so to achieve a given amount of dilution, you can remove one CO2 molecule or add 2500 other molecules.
Finally, I don't know what the side effects of increasing global air pressure would be, but I'm sure there would be significant effects!