RCS and Amanos seem to be fine with hard water. But it is your choice and targeting a good GH and KH is not hard and might help with your neon tetras and cories.
I would say, start by doing only small (20%) changes until you reach your target GH, your KH might still be a little up. At this point start remineralizing the water, target optimal parameters for the volume of displaced water only. Larger water changes can be done now. Your KH, GH will stabilize in time. You can of course mix RO water with tap and until you get your target. Since your KH is double your GH, I would set my RO-tap target for a certain KH and then add some extra GH boosters ( Salty shrimp GH+ , Shrimp King Bee Salt , Nilocg GH Booster etc)
As others mentioned, once you have your mix % set for a certain GH KH you can check with your TDS meter. Afterwards, reaching the ~TDS value from the same mix gives you a fast and cheap confirmation that everything is good, without the need to test GH, KH every time.
A RO unit with functional membranes and filters should give you a TDS < 10 , not much can be in such a small TDS
On hiatus till later this year