I’ve got a Green Leaf Aquariums 2 stage regulator, I operate my CaRx by injecting enough CO2 that the effluent of the reactor is 20+ dKh. I use a peristaltic pump (an old analog Cole Palmer from ebay) and the effluent rate is about 60 ml/min (my tank is very high demand). I then wait to see what the tank dKh settles at. (usually about a week later). IF it’s lower than it was I’ll inject a tiny bit more CO2 into the reactor. (The solenoid is always on, it never clicks off). Then I’ll wait a week and test my dKh again. If it’s too high, I’ll adjust the needle valve on the regulator the tiniest bit down. This has been a very reliable and stable way for me to operate the reactor, I rarely if ever need to make an adjustment. The trick is to make singular adjustments when you can, try not to adjust multiple variables (flow rate and CO2) unless you are really far off the mark.
Getting it dialed in initially is the tricky part, once you are close tiny little adjustments are all you need. Go slow in the beginning and try not to make more than a single adjustment every 24 hours or so. I also think it’s more important to have a higher dKH in the effluent than it is to have a high flow rate through the reactor. My 60ml/min is probably pretty high for most tanks and I run a large reactor (a GEO 8”x18”).
If your using a pH probe I wouldn’t let it control the solenoid, at most I would use it as an arbitrary visual idea of the changes you are making with your tiny adjustments (realizing it’s readings are going to drift over time). I don’t count bubbles from the regulator, because the whole system is stable enough that I don’t need to.
Over the first year the only time I had to adjust the reactor was after changing the CO2 bottle

It’s been a very stable carefree way to operate it. I hope this helps