I can't really help with the water softener, although the resulting GH and KH looks weird to me. I heard that using potassium instead of sodium would be a great advantage if you use the softened water. Personally I think the resulting water could be very unbalanced.
Anyway, the problems with your plants could be signs of nutrient deficiencies. You have good lighting (not sure how good your reflectors are...) so that part is creating a lot of --potential -- growth. I would wait with dosing phosphorus and nitrate, and first think about Iron and Trace elements (I use Seachem products for that... pretty simple), and Potassium. Ideally you would start to dose one thing, and observe maybe two weeks to see if there is a difference, then start with the next, etc. If you start dosing EVERYTHING at once and you get problems, you don't know what it's caused by.
If that works, your plants will grow better and algae will start to go away.
You might want to ponder about CO2... with hard water you will get excellent results, most if not all plants will grow faster, bigger and greener almost immediately. If you think about switching to softened water to improve plant growth think again and consider adding some CO2 instead.