Wonder if a fully functioning fish take would be even better - if you get plenty of plants growing, they will feed off the water/each other in my experience. The rate of air injection would likely have to be higher than that of a normal fish tank though? I used to run a fish tank with CO2 injection to get the plants growing well. The best, cheap way of doing this was to put CO2 into the filter intake, that way big bubbles which escapes the diffuser were blended up by the impeller of the filtration.
AFAIK you could introduce mosses (Vesicularia and the likes) instead of higher plants, they're not as CO2 dependent. Every aquarium tutorial I ever read tells me that air pumps lower the CO2 content and you need injection as you explain.
A cheap air pump for an aquarium will produce enough pressure for a string of air stones. I have a 10$ pump (2W) on my desk here that blows 4 stones and I still have to limit the flow a bit or the display looks more violent than soothing. More expensive pumps not only have more power but will also have a better design with less noise.