@LoopSki when we moved into our house it had a well system as the source for water with similar issues. Hard water and lots of iron. The house had a BIRM filtration system right downstream of the expansion tank to remove the iron and then and old water softener right after the BIRM to soften. Our BIRM system consists of 3 tanks. The first tank injects atomized compressed air into the tank while water is being introduced. The first tank should never be more than half full of water to allow sufficient oxygen water blending. This is key before the water travels to the next tank where the filter media is present. The water containing iron flows through the media, if there is enough oxygen in the water, the Birm causes the iron to form rust, or solid iron particles. After these rust particles get trapped in the filter media, once or twice a week they are automatically backwashed out to drain, and the filter media is ready to filter again. Depending on your iron levels you can set the backwash to run as frequently as necessary. Ours runs every other day. The 3rd tank basically has a float valve/vent on the top that allows any remaining oxygen to escape so your faucets don't sputter with air.
I'll be honest, it took me a long time to get it all figured out and at one point I had Culligan come out and quote a replacement system just as you did. $5k was more than I wanted to spend. Once I got the system figured out and balanced. I only had to replace the media 1 time in the BIRM filter tank and that was only about $200 ~ 5 years ago. As long as the backwash runs when its supposed to, the iron is removed and the media stays fresh. We did install a new waterboss softener with Iron control about 3 years ago. We always use the Morton Rust removed salt pellets. That helped with the water hardness.
If our system ever fails, we know it within a day as the water starts to develop a very metallic smell to it. I'm sure newer systems may be more compact and have more technology but what we have works well once setup properly. Hope this helps.