Some states require a brake inspection and use a brake dynamometer to test simultaneous braking force at all four wheels. If you can put your truck on such a machine it may narrow your search. I hope you post it here if you find your problem. Sometimes what should be a simple problem takes forever to figure out.

 

Seems like you've gone through most of the common sources from the brakes, I would doublecheck the front suspension just to be on the safe side. Normally a suspension pull would be al the time, but application of the brakes may cause a little more stress on a marginal weakness in a suspension part.

 

I agree with toyo. Maybe it's time to look past bad brakes and check all bushing on the spindle arms. Maybe the forward force that is applied during braking is causing a missalignment to occur. My 75' F150 lost a rubber bushing from the torque arm that attahes to the spindle arms and would allow the spindle to slightly move front to back when I would switch from going forward to reverse.

 

I'm thinking you may have something on or wrong with that l/f. I know you said you clened all but it sounds like something there is making the pads grab. When you switched it moved to the right for a bit then back left. (like something got on pads but after moving they cleaned up)
Then again it could be just bad pads.