As much as I would love to flip to bypass, its a whole home system so my hot water heater if full of it as well. So draining the lines I don't think is possible.
On bypass your cold water will be good and some salty water from your heater will be mixed with it so at least the salts are minimized a bit. I have a water conditioner but I use KCl which is actually benificial to your plants but you might OD on K which can block the absortion of other minerals. But if you could switch to KCl (check if your softener can run on KCl) then fill on bypass then its a mix of regular water and some with KCl from the hot water tank.
What I do is just condition and heat my water in a 18Gallon tub. I fill it with bypassed cold water and heat, treat (prime, Mg). Not using any water from the hot water tank eliminates the extra metals and contamination. I also used to let the tub sit a week to gas out so I don't have to use Prime. I also have my tub on a high ledge so I can use the hose to fill it and use the hose to transfer the water from the tub to the tank