...Just brainstorming here:
1) Ion exchange up front to get rid of the hardness and the acid gases. Removing the acids will automatically adjust the pH. (SteveR, will a domestic water softener get rid of anions? I only think of it in terms of calcium and iron.) You can buy anion softners but the normal residential unit is cation. I don't know how much acid will be removed/neutralized in a cation resin water softener.
The OP did not state the hardness but when an acid neutralizer is added to the system a cation softener will be needed to remove the Ca and Mg added to neutralize the acid water.
2) followed by chlorination. Ozone is fine, but it leaves no protective residual. If you chlorinate do it after the softner as the chlorine will degrade the resins. It would seem chlorination of the well (shocking it) might be a short term fix for the current bacerial problem. The coliform load is high but the E. coli count is zero which might indicate a non-human source of the coliforms which would usually rule out contamination from a septic field. If this is the case, then shocking the well might knock out the contamination.
3) followed by activated charcoal filter to get rid of organics, chloramines left over from the chlorination step and act as a filter. You probably will have to change this often. Maybe add a string filter in front of the charcoal filter later if the charcoal plugs up too quickly. This may be overkill in a residential system. Also, the carbon will remove the chlorine residual and can create a microbiological soup in the carbon filter. The OP already has issues with bacteria and family sickness so I would opt out of the carbon filter.
Water treatment equipment likes to run at a steady flow. I am thinking that all this would be upstream of your tank.
SteveR, does this make sense?