You are right that there has not been much follow-through at Public Lab on developing and testing DIY conductivity or total dissolved solids (TDS) sensors. Part of the reason for that is the difficulty of making a reliable sensor. Calibrating the sensor and getting it to provide consistent results for more than a few days under water are serious challenges. A good attempt is here, but there is not much info about successful deployments.
Your goal of making a data logger with TDS sensor for $20.00 is ambitious. You can buy the basic parts for a Cave Pearl Logger or Mini Pearl Logger for about $10 if you order everything from sellers in Asia. You can probably make a TDS sensor from basic parts for another $10, but some of the challenges (low voltage, alternating current) might require a complex design and careful sourcing of components.
I have tried the DFRobot TDS sensor with a Mini Pearl Logger and it seems to have potential. I have only tried it in a spring house and I think the water there is so clean that most or all of the variation in the TDS results is noise. More testing is needed. That sensor costs $13.00 which is a very good deal considering that it apparently has both the low voltage and alternating current features.
Ed Mallon's focus with the Cave Pearl Loggers has been to get them to last more than a year on small batteries. This requires intricate modification of off-the-shelf components and complex code to sleep the components between logging events. The Mini Pearl Logger uses a different approach to longevity and uses an external low-voltage timer to turn the data logger off between logging events. It is much simpler to build and program. There has not been enough time to determine if this provides comparable longevity. Do you need longevity?
Are you going to deploy the loggers in drilled wells or test the tap water? If the latter, maybe you don't need a data logger and a hand-held TDS meter would be sufficient. That is even easier to build from an Arduino Pro Mini, and does not involve the heartbreak of multi-week deployments of faulty loggers. But maybe your plan is to monitor the live data via radio so faulty loggers will be identified. That will be even harder to do for $20 per logger, although maybe not impossible.