I think you can make a pretty accurate guess, and avoid the calculus, if you have some idea of how quickly pollutants (nitrates, whatever) are building up in your tank.
I'm thinking that using a drip overflow system, you want to eventually have the amount of pollutants leaving the tank be equal, or very close to the amount generated by your tanks occupants.
Just for the sake of argument, I'm going to make up some numbers. Say, after a week without any waterchanges, your tank has ~100ppm NO3 in 40 gallons.
Assuming the pollutant generation rate is equal, you're tank is building up 100ppm over 168 hours, about ~.59ppm/hour
Adding a gallon of water to the tank over the course of an hour, and allowing it to over flow should remove pretty close to 1/40th (2.5%) of the tank volume, and with it remove approximately 1/40th (2.5%)of the current buildup of pollutant.
Things should about balance out when you have about 24ppm or so, as 2.5% of that is about ~.6ppm. If NO3 level in the tank is higher, more will be removed with each gallon, so it should gradually approach the 24ppm balance.
This is a pretty rough estimate, and is only considering rates, and assumes constant addition/removal of water and pollutants, but you should be able to get a fairly close estimate based on previous NO3/TDS counts. It's been quite a while since I've did any of these types of problems, so there is a very good chance I've overlooked or omitted some important detail.