Tool shaped like a thin-bladed putty knife but with a rubber blade and spongelike surface

Someone told me to drain the tank. Then put duck tape over the holes under the rim. Add your cleaner of choice to the tank, (I poured directly into the bowl filler part as I was "flushing"). I used CLR. Let it sit for 30 minutes. Opened up the holes pretty well. Did it again. Flushes like new. I have HORRIBLE water, rust, iron ect. Give it a try. This is not spam, nor do I want to spent hundreds to replace it.

Most likely, the thick top cover can be removed very easily. F.e. after removing 2 screws, the cover must be slided back- or forward for some few centimeters to be lifted up.

Before removing the cover, the power plug and/or breaker has to be disconnected.

Since there may be live/hot parts (high voltage) beneath the cover, it is important to check that there is really no more power connected to the machine.

Without this cover, all parts of the water flow into the conditioner side should be visible and easy to be cleaned. If the material is made for high temperature, a steam cleaner may help. Or a tooth/dish/pipe brush. If the clogged part(s) can be removed, a dish washer could help cleaning those parts with hot water.