Chopping is a very efficient way to dissolve CO2. Based on what you have said above, I think you should turn up the CO2 a bit. 6hrs for a drop checker change is too long, IMO. I don't know what your bps count is.
Remember, your initial post said you didn't think you were dissolving enough CO2. I felt your bps was too low. If you turn up the gas, the seltzer water effect will get worse. You posted in the begining that you don't care for this look. I don't either.
So, in order to add more gas, but reduce the 7-up look, you have to get a reactor, and add CO2 after the pump.
I had a similar dilema with the 7-up look. I wanted to maintain the CO2 saturation, but reduce the bubbles. I stopped chopping, and added CO2 after the pump. It seems to work.
You don't have to get all fancy with the CO2 line into your reactor. Just drill a small hole in the outlet tubing from your pump (just past the pump barb) so you can stick the CO2 tubing into the hole or use a connector barb from the sprinkler dripper systems and stick it in.
Remember, the reactor is not going to help much for micro bubbles (at least not enough for you to see the difference). I tried with my reactor. Reactors are for big bubbles.