I would think algae would lower the TDS readings as they're consuming nutrient. likely the change your seeing is from the plants consuming the nutrients. I believe the leveling off is due to either the plants are now transpiring more than consuming nutrient and / or they're not consuming as much nutrient that dramatically affects the TDS readings. I.e. southernAG's forumula is rich in Potassium (K) and will only use as much as it needs and leave the rest in solution. (it is likely being restricted by some other nutrient or lack thereof)
As for your fish inquiry, it is my understanding that high TDS is a primary restriction of aquaponics and that is why Tilapia are normally used because the can live in above normal TDS levels.
Does the nutrient stay in the kiddie pool for long lengths of time?

You're always going to have algae problems in that system. As long as nutrient water gets hit by sunlight, everything will turn green. There is no practical cure, except to block the sunlight. You could buy a UV sterilizer, or they even have ultra-sonic algae destroying devices. But it would be a lot better to just block the light. Even the light going through the blue plastic of the kiddie pool will be enough to grow algae.

I guess that the best way to control algae and maintain a correct nutrient balance would be to drain the system and start off ith a fresh batch each week.

Even when you drain it, the green goo will still be left behind. Blocking the light will be the only cure that doesn't frustrate you. You could glue aluminum foil around the outside of the kiddie pool, or the black rubberized spray undercoating for cars works ok, too. Then I'd try to make a lid out of foil-faced styrofoam sheets. An imperfect lid is a lot better than none at all.

I am able to isolate the pods and will just blast the algae away with the water hose for now.

I replenshid the water in the system. It took about 50 gallons. The TDS reading dropped from 720 to 500. Adding a 50 gallon strength nutrient mix, the TDS reading came back up to 720.

Chuck,
Is that an ebb n flo system or do you keep the water in the pool all the time?

Generally speaking, fish suffer in water with more than 40ppm nitrate.

Generally speaking, fish suffer in water with more than 40ppm nitrate.

OK, Thanks for the input. The pools drain down to a depth of around 2 inches and fill to about 5 inches over a 10 to 15 minute intervals depending on the total amount of water in the system. It will operate with as little as 45 gallons total, but the cycle time is around 15-20 minutes. When there is around 100 gallons in the system, it cycles in less than 10 minutes.

Perlite is the main growing medium in use. Some pots filled with a fast draining potting mix sit in a lower pot filled with perlite and act as a wick. Other pots have plants growing in perlite. This system was built as an exeriment to see if a single system can be used to grow both hydroponic and soil based plants.

So far, the piggy-back soil based pots that sit in perlite filled pots seem to be doing fine. So far, after around 3 weeks, there has not been any evidence of problems of too much water in the soil to adversly affect growth and production. The plants that are growing in the perlite are also doing well.