@wd8dsb,
Don, yes your softener sounds as if it may be undersized but no one can tell you what size you need without more info.
It may also be that it simply is not set up correctly.
A softener is sized based on the hardness, iron and manganese and then, the number of permanent family members and bathrooms and the type of fixtures in them. Which gets to your peak demand flow rate that the softener must be able to treat.
The softener's constant SFR (service flow rating) gpm is dictated by the cuft volume of resin in the tank. Every time the SFR gpm is exceeded, the softener can not remove all the hardness.
Which sounds as if that is your hard water problem before the unit regenerates. Or you've left it run low or out of salt and it hasn't regenerated properly once or more often.
What do you have the salt dose set at in lbs or minutes?
What K of capacity do you have it set to?
What if any reserve percentage etc. is it set for?
What does Qualitywaterforless say about this? Did they size the softener for you?
Did they tell you how to set it up (program it)?
As to your salt tank problem. If you are using solar crystal salt, there should be no build up in the tank. You get mush with pellet or block type salt, not solar crystal; it totally dissolves.
You want to be careful using hot water on the plastic parts in the salt tank, and the salt tank itself. Plastics and hot water do not mix well.
Another thing, this idea of adding salt just so some is above the water level... you'll be adding salt quite frequently but, many softeners do not have more than 2-3" of water in the bottom of the salt tank between regenerations.
Your big box brands are like that and there are others like those I sell. They also use softened water to make brine with, I'm not sure your 5600SXT does both. It's called Pre brined, the brine make up water is added at the time of the regeneration and used during that regeneration. Not added at the end of a regeneration to sit there for a few days or a week until the next regeneration like most softeners do.
Pre brined keeps your salt tank cleaner and there is none of this once a year disconnecting and dumping the salt tank to clean it out silliness, unless you use pellet or block salt... and especially potassium chloride salt. Which if you use potassium chloride, it requires a higher salt dose in many cases because at higher salt efficiency settings, it is not as good/efficient as regular sodium chloride. And it costs 2-4 times as much for the same size bag, if you can find it. Regular solar crystal salt looks like 1/4 x 3/8" gravel sized pieces or course solar salt is like 1/2" x 3/4" crushed rock pieces.