Some softeners may be better at rinsing than others. Some noses are less sensitive to that smell than others.
I would especially use IO for a remedial treatment, where you make a stronger solution, and then stop the flow at the right time (bypass can do that). Then let the IO solution sit with the resin.
Later, take the unit out of bypass, and do an extra regen.
Experiment for you: when the salt is way down, look at the water level in the brine tube by shining a light down the tube, and seeing where on the translucent tube the water level is in the tube. It is usually higher than the liquid level in the salt area. Mark that level if you can.
Then gently stir the salt, which will mix the upper layers with salt. Wait two hours. Has the water level risen? If no, the water was saturated with salt before you stirred. If the level rises, the salt was not saturated before stirring. In that case, stir again, and see if you can see another rise.