how important is it to match the CFM?
Very, as you well know.
I feel like there's more to the "quiet fan" technology than "just make it shift less air", but the quieter ones definitely have lower CFMs
You sound like you are getting stuck on what you
want to believe toward the solution that you
want.
Recommend you concentrate on the fundamentals. You have a CPU that runs at a certain temperature - can you not monitor that?
You have a CPU with a knowable operational temperature range (overclockers go nuts about this stuff). You need those numbers AND you need to know how close or far you are now, with the working, albeit noisy, system.
Nobody can tell you the precise relationship between CFM and temperature unless all (or most) of the other factors are kept constant - it is reasonable to think that you can keep all those factors constant since you have one system in a room. Given that case, how can you vary CFM?
I'd install a high-airflow fan and throttle the speed down and watch the temperature.
So, if you can figure out how to increase or decrease your CFM via messing with PWM or something even simpler, then you can see what effect it has on temperature. A SPL meter can be used in concert with the manipulations. I agree with the suggestion.
Too much? Then buy the quieter fan and wait until the CPU overheats. More seriously, if you monitor CPU temp and know the max recommended temp, you could watch it and have a good idea, before it shut down.
You may also be able to add to other areas of the case fans, but that seems somewhat indirect to me.
I can't believe you can't measure CPU temp!