Jeff wrote:"TDS" as measured with a refractometer is the refractive index of the sample, run through a formula, that gives a reasonable approximation of the total dissolved solids in the cup. It is a rough measure of the "strength" of the coffee.

I think it's a lot better than a reasonable approximation of the dissolved solids concentration. The VST refractometer has an accuracy of ±0.05% in the espresso range of 5-20% TDS. That doesn't sound like a rough measure to me.

You could try fractionating one of your shots: take 3-4 small cups and sequence each of them into the flow as the shot proceeds. Each one will have a different TDS/flavor profile that can give some insights into how to dial in the overall shot.