Hey, I have some personal experience with this one. We also have EXTREMELY hard water. Like, crazy hard. We have a water softener, and since I couldn't find any good resources about how it would affect my betta, I tentatively used it.
Bad idea. The day after my water change, I noticed strangle little bits of stuff on him, little white weird hard-looking things. He acted normally, swam normally, ate normally, but I quickly went out and bought some spring water for him instead, and after his water change they disappeared. I will note, that I did use water conditioner with the hard water, and it didn't seem to do anything.
What I've done since then you may not be able to do, but it's worked great for me all summer. My family has a cabin with an artesian well, so we have really clear fresh spring water. My dad brings me home a couple gallons of this water, that I let sit for awhile before I use, and I mix it 50% store bought spring water, 50% of my well water, and add water conditioner to it (just in case). The water has never stayed clearer, and my fish has never seemed happier!
Buying water can get expensive if you need to do it long term, so I would suggest if you can't afford it all the time, at least mix your water with some spring water? Hopefully other people will have suggestions for you!
Even if you have a friend nearby with better water, maybe ask if you can come over and fill some large jugs with water? (I think I usually get 2, 4 gallon jugs at a time).