Here's another idea -
HotSpring dealers (I used to be one) sell an item called "Vanishing Act." It is a one-use softener, and it comes in two sizes. Open the box, and you will find a 'pillow' which is actually a bag of softener pellets. You simply place that bag on the bottom of the Hot Tub - right over the return fitting. 24 hours later, test the water hardness and you should be good to go. If not, leave it in place a second 24 hours.
The part I'm not fond of: after
one use you toss the thing. Yes, I have had customers who have soaked it in brine and used it again, but I don't know how well that worked and can't vouch for their results. Might be well worth the effort!
Vanishing Act - available at your local HotSpring dealer, part number 76029 prices range a LOT - from $32 to $50 so shop carefully.
HTH