This is a difficult fix because the first part of troubleshooting a valve that has 20 years on it is to start with rebuilding the head with new seals, spacers, piston, and drop in a new throat and nozzle, a couple seals etc. Unfortunately you have a proprietary valve that does not make this an easy fix. Most of the companies will not sell you there special parts because they want to send a "technician" out to try to sell you a new unit.
That being said, the problem you are having is not common, but has been known for many years. If it is not the seal and spacers, the injector assembly works on a venturi, for this to work, the nozzle water must not shoot perfectly through the throat. It needs to hit the sides and cause a water seal and thus create suction. This is why Fleck added the "Air Disperser" as they call it to the injector assembly years ago to most of their systems. It is a very rare occurance, and since your unit just started this, it is not likely the problem. The only reason I go there is because you say you get good suction when you cycle the bypass valve, this would disrupt the water flow through the injector likely making a good venturi affect. A very old trick (prior to the "air disperser" was to tweak the throat on the injector, or to make an imperfection on it that wold do the same thing as the air dispersor. In my 25 years, I have only had to do this maybe 10 times. I used to rebuild up to 6-8 softeners of every brand per day. In all reality, a 20 year old softener should be considered for retirment and it should be replaced with a non proprietary system so parts in the future are not an issue. Even the tank thread on your system is proprietary making a valve swap impossible. Many years ago we made an adapter to change the tank to a standard control valve thread, but that was too expensive and very prone to failures. It has since been discontinued.