Why not just have one fermzilla or keg with sugar and yeast in and a spunding valve on it on a T with the other limb going to your kegerator or keg that you are purging ( or combinations therof). When CO2 production slows just inject a bit more sugary water and yeast nutrient in. Or you could just ferment it to the highest pressure your Corney would take and then use an inline regulator to your kegerator / keg you are purging.
That's an interesting idea, using a corny keg as a fermenter of sugar wash+scads of nutrient. Many folks have stated that several types of yeast can handle pressures in excess of 100psi, but their beer making flavor performance is reduced. Wouldn't be a problem for just making CO2 tho, and pretty cheap.
I too am keeping this idea in the playbook for the next CO2 supply shortage! LOL
Cornys (the cans themselves) can handle over 130psi, and most PRV's on the ball locks are the grey 100psi type. The next most common is the green PRV, which blows at 65psi.
For the sake of a thought experiment, fill the initial "gas storage keg" with water/starsan. So full that you have only a few mL of headspace filled with air mix.
So, say you did a gas to gas jumper from the ferm vessel to this storage keg initially:
Pressurize the tiny amount of headspace in that liquid tank. Doing it this way would reduce the purges needed to get the headspace O2 concentration down pretty low (math fails me on Monday evenings, but I'm sure this could be calculated using post #3 and a good pot of coffee). You'd also lose A LOT less CO2 gas by purging that headspace first.
Then add the bev to bev jumper from the storage keg to either: 1) another keg or 2) a bucket large enuf to hold the purged liquid. Homer buckets and their ilk work.
To maximize the CO2 "stored", you'd have to remove the bev jumper once all of the liquid (or as much as you can get) has been purged. Then you can spund it to 20, 30 or even more pressure, all depends on how well you can keep that initial fermentation managed.
In that situation, I'd switch to a ferm-gas to bev-keg jumper, and spund off the gas port on the corny to avoid any lingering liquid from mucking up the spunding valve.
I suppose you could use a non-liquid filled keg, it would just take a longer fermentation or just multiple fermentations. One to fully clear the keg down to 5 parts per billion O2, and then another fermentation to pressurize the vessel. There would still be some O2 getting pushed out of the fermenter during active fermentation, and this is where the diffusion calculations get way over my head. If you give it more time, and more CO2, you could get there.
The fermenter you are using is rated to about 35psi, so you wouldn't be able to use the corny to its full rating, but it does seem plausible this would work.