If you can drain and refill for ~$120, that's definitely the way I'd go. Because you have some scale, I'd recommend doing a 100% drain, and NOT adding any calcium or alkalinity (baking soda) for awhile. If the pH is too low, use borax to raise it. That way, you have the option of running a low calcium low pH pool long enough to soften and then remove the scale.

I would call the water company though -- they can have some funky ways of calculating bills. And, get the name and position of the person who helped you. That way, if you get a bill next month for $400 because of some bill-calculating funkiness, you can credibly do the whole, "But sir, I was told by your staff . . .", etc. routine.