Here is where I think you are at:I fully agree. I believe I have taken the steps outlined in that post and have indicated what I found. I am not sure what step to take next.
I think you have eliminated loose brine line connections by successfully sucking.If no water flows out the hole... the most common causes of too much brine in the salt tank and no suction, is loose brine line connections, a blocked injector, injector screen, or drain line kinked etc.. There is a connection under the valve that has the float hanging on it in the brine well in the brine tank. It holds the brine pickup tube up into the float valve, then there is one on top that valve and one up on the elbow on the control valve. Hand tight plus a half turn with a wrench or pliers and stop.
I think you have implied water flows at a high rate during the backwash cycle, If so, that would have eliminated drain line kinked. That would seem to indicate that you should remove and clean the injector and injector screen. I am just interpreting what I think is being said. I have not even seen a Clack myself AFAIK. Take pictures as you get in there in case you want to post them to show your success or lack.
Now if you do that and find they are OK, I don't know what would be next. But at last do the injector and injector screen.
Regarding the warranty via a different dealer, I don't know. Do you have the original receipt? That would seem to be important if you were to pursue that. Even then, there may not be coverage... no clue.