A SWCG will certainly work. I only installed a small water softener this past winter, not for the SWCG, but so my CH levels do not rise so fast as my wife does not like the water when it gets a CH of 800+. It is a RV type softener that I do manual regeneration of about once a month. It works OK, but not as good as a whole house softener.
Managing your CSI to between -0.3 and 0.0 is quite doable up to at least a CH of 800 ppm. It takes diligent management of TA and regular addition of acid to control the pH and TA rise due to fill water addition. The use of borates can also reduce the scaling tendency in the SWCG cell.
I have never cleaned my SWCG of scale with acid. I look at it every spring and have pushed out a chunk of scale or two with a popsicle stick, but have never had significant scale on the SWCG.
With out softened water, you will have to plan a full water exchange about every 2 to 2 1/2 years in Las Vegas I suspect. Here in Laughlin, I would have to exchange my water out due to high CH every 18 months or so.