Nice write up. I've been using lime for at least 2 yrs now. My water is also high in Calcium so I typically don't add any back. I do add some CaSO4 in my Alt and IPAs, but that's it.
I treat my water in my boil pot. It holds 10 gal and the spigot make it easy for me to drain it off. I typically set up my water the night before I plan on brewing and it will have settled by the next morning.
One of these days I will do the experiment to see how long it takes to remove the temporary hardness simply by aerating. It works by the same mechanism as boiling - reaching equilibration with the CO2 in the air, it just takes longer. In one ref. I read, they mention this, but didn't give a time frame. I'm envisioning that if it were less than a week, then I could set up a large container with water and bubble air through it and then a week later, drain off what water I need, and then just top the reservoir off and let it bubble until the next brew day. Presumably, the more bubbles/air the faster it will reach equilibrium.
Evaporation might be a concern (concentrating other salts). I've thought about running the air through a container of RO water first before the tank to saturate it with water to minimize water loss.
One of these days I'll set up the experiment