I would contact Andy at Softenerparts.com. He's a wealth of knowledge and sells all the Fleck parts and could easily tell you what you'll need and how much it would cost - or if it's even worth doing.
My home has Fleck 5600 controls for both the acid neutralizer and softener. He's been extremely helpful, he's very responsive to emails, and his videos on youtube show just how easy the Fleck is to overhaul. Gave me the confidence to tear into my 10+ year old controls and replace the seals & spacers, a bunch of o-rings, and clean out the filter screen. I figured as long as I'm going to open it, I want to basically overhaul it. It's really a piece of cake to work on.
In retrospect, even though the parts were relatively cheap, I should have called or emailed Andy first.