"One way I have cleaned out a duct like you have is to use a leaf blower. Just disconnect the dryer and insert the business end of the leaf blower in the hose and let her rip. After a few minutes it'll look like it's snowing outside! "
That is funny AND a good idea.
Yeah, I wouldn't even bother with messing with the sensors. You've found your problem. It's in the walls and attic. You need to do a complete cleaning of those ducts, or pay someone to do it.
You really need to find out for your own sense, where the duct terminates. You may need to climb on the roof. If you have a roof cap and someone had a new roof sloppily put on, they may have damaged the cap, and that is what's caused the problem.
If you have a soffit vented duct, you may have birds or squirrels that have tried to nest in it, and that may be what's caused a jam.
Thanks for the pictures. We really appreciate them.