CaRx media will begin to dissolve at a ph of about 7.6, it will dissolve slowly at that PH, and given that you don't have a high demand for alk, you want the media to dissolve slowly. You have two ways of controlling the alk output, the ph in the reactor, which controls the dissolution rate of the media, and the effluent flow, which controls the amount of alk dispensed. Running the ph so low is causing the effluent to be very rich in alk, so you have to have a very slow effluent flow to keep from adding too much alk. Raise the ph and raise the effluent so that it is a broken stream (which it appears you have already done). Once you get that broken stream, you slowly lower the ph to the desired alk output.
I have the same situation, my reactor can put out a lot more than my alk demands, so I have my ph controlled at 7.3 and the effluent flow a broken stream which is about 6-8 drops per second. I do not change the effluent flow, just the ph in the reactor. I use ReBorn media, which is large media and it dissolves just fine at a higher than normal PH.
Don't make it harder than it has to be. Many of us here have done it this way for years, and it is the easiest way to let the reactor function. Too slow of an effluent stream will only clog the effluent valve, you don't want that, it is a pain to deal with. As your alk demand increases, just lower the ph a point at a time until the alk consumption is in line with the reactor output. What you are doing now is the same thing as trying to keep a car at 20 mph and any time it drops below that, you are flooring the accelerator just to increase the mph slightly, which shoots the car past 20 mph and the engine has to be stopped to allow the car to slow back down. Keep the accelerator pressed just enough to keep the car at a steady 20 mph. Quit flooring it.
Smile and enjoy the tank instead of working so hard to keep the reactor in line with demand.