I believe in reversing the rotational direction on regular rotations. If a set of tires had NEVER been rotated in 40,000 miles or so, I might not do it, but I believe there's a benefit. The tread blocks get a "tooth" to them that reversal will smooth back off. Then it forms in that rotation direction. That's part of the reason old tires may seem noisier. They are, because of that pattern.
I was lucky to spend nearly an hour with a couple tire professionals. They showed me a lot and told me a lot. One thing was that if front tires are edge-worn, a move to the rear duals should include putting the worn edge next to the other dual tire. In our case, fronts were edge-worn on the inside ribs, so they had to be "flipped" which also reversed rotation, to get them into that position on the rear.
All that said, my understanding is that Ford doesn't recommend rotating the rear tires on a routine basis. But I like rotating the fronts, especially if a spare can be worked into a three-tire pattern.
If God's Your Co-Pilot Move Over, jd
2003 Jayco Escapade 31A on 2002 Ford E450 V10 4R100 218" WB