...there's no way for what I deem sensible money to source a meter that will continually monitor CO2 levels in the aquarium.
I think the "continual" bit is the issue. Any system that works by the continual leakage of ions is going to give problems long term, so you really need to use a solid state option, and to keep it isolated from electrical interference (like Marcel's @zozo
You can get "standard" meters and probes that will give you accurate measurements, but you really need to re-calibrate them fairly regularly, and store the electrode in the appropriate storage solution.
If you have very heavily carbonate buffered water (or very salt rich water) then the problem lessens, as you move towards pure H2O the problem intensifies. The issue then is that you then know the pH is going to be pretty close to pH8 in heavily carbonate buffered water, and it isn't going to change very much.
Because I use rain-water (about 120 microS), I'm not a CO2 user, run low nutrient and have very "weedy" tanks, I can predict the pH level in the tanks, but they don't really tell me anything that I didn't already know. During the photoperiod the tank is fully saturated with oxygen,CO2 depleted and the pH is somewhere around pH8, first thing in the morning it is around pH7 (more CO2, less O2). I have shell attrition on the snails, so sometimes pH must dip below pH7. As flow reduces the amplitude of the variation will rise. It is back to <"the pond
The <"Sands-Jensen paper
">, linked into <"latest pH profiles
">, makes interesting reading.
Some methodology bits
When I started searching for a standard set of methods, and parameters, that allowed you to characterise the health of your aquarium I actually started with pH, because it is so important. I hadn't realise how much pH would vary over a day, and I didn't know that CO2 injection was a thing.
When I found out about the pH drop from CO2 injection I knew I needed to look at pH measurement and stability slightly differently and after a while I began to think that actually I needed to abandon pH measurement all together, which led me to looking at conductivity, nothing like as useful, but easily consistently measurable with relatively cheap kit.
It was the same with nitrate (NO3) measurement, I really want to know what NO3 levels were in the tanks, but it rapidly became apparent that there were issues with NO3 measurement. That was what why I went back to the Lemna
bioassay, re-configured as the <"Duckweed Index