Thanks, Wade! I have actually tried the resin cleaner already. I've done it a few times. The interesting part is that I got soft water for a short period of time, using just the cold water, and then it stopped. Right now I think the water is kind of soft, but coming down from a 25gpg by a little isn't much.
I honestly think that with the trouble-shooting I've done, I'm left with nothing other than the resin needing to be changed out.
I believe I should be able to put it in bypass mode, disconnect the back where the in and out connect to the bypass unit, pull it away and then remove the motor/head off the tank. Then get the tank out, remove the distributor, pour out the old resin and put in the new.
I'm not sure of the age of the softener, but the motor and the valves seem to be working exactly the way they should without problem. I have done regeneration a few times with a cleaner, but it still doesn't seem to be much of an improvement (maybe slightly, if at all).