Keith, since we both live in Phoenix this may be what’s wrong. When the softener was added to your home the line into the front of your house was cut and then a new copper supply and return plumbed all the way around to the back of the house to the location of the water softener. I believe that this run of pipe beginning and returning to the front of the house would be 80’+ or so. The line supplying your house is 3/4″ copper and so would be the divert run, you are dealing with friction pressure loss. This is why bypassing your softener won’t make much difference since the bypass is where the softener is. Since we never freeze in AZ the installers of this system just dropped some pipe in a shallow trench. This is easier than plumbing through your house it’s a longer distance around your house than through it also a lot cheaper to install it this way but it sacrifices your pressure. I would call the AZ registrar of contractors and place a complaint against the company that installed this system in your home. I have seen this type of install done in many homes. Unfortunately in AZ we have many fly by night company’s that end up doing these types of installs. I am sure that no building permit was used for this work.
Respectfully David F. Walling