Reduced TDS without RO?

We have a reverse osmosis system (RO) at our kitchen sink and a charcoal based filter for our refrigerator. When I prep water for the coffee maker, I typically do about 1/3 RO water to 2/3 fridge water, which gives me a rate of 150 TDS (total dissolved solids), ideal for making coffee as I understand it. I also tend to mix RO and charcoal filtered water for drinking as I find water with minerals to taste more natural than pure RO water.

That said, the fridge line still has a TDS of ~225-250 TDS, which results in chalky sediment coming from the ice maker. I like the charcoal filtration, which removes a pronounced level of chlorine in the line along with other impurities, while it leaves fluoride and other minerals intact. My question is, is there any non-RO solution that would reduce our default TDS and help us maintain the minerals (including fluoride) in the line, while helping us resolve the issue of chalky, sediment-laden ice?

Offhand, I've wondered about splitting the line, having half be regular tap water and the other RO, and then combining the line after the fact to give a lowered TDS, but I don't know how feasible that is.

Thoughts?