Ok, I have to first qualify my remarks so folks understand where I'm coming from (any fishkeepers will immediately grok me on this, I think). First, I have no experience running any kind of water cultivation of terrestrial plants. I HAVE kept aquatic plants, and of course fish & inverts. So I see things with 'fish-eyes'.
Second, it's important to understand where the CO2/O2 gas exchange occurs, and that is, outside of a venturi scenario, ONLY at the surface. That is specifically why fluming works so well, it creates a huge amount of surface agitation and turbulence, thus enhancing the gas exchange (the exchange of oxygen and carbon dioxide molecules, back and forth, til they reach an equilibrium).
So! Even if you're getting large bubbles, it seems to me that if you're getting good surface agitation then you're getting good DO (dissolved oxygen) levels, and that's what you're after here, yes? Maybe the airstones are really extraneous here.