My intermediate solution was to lay the posts and thus the fence on the ground to create an opening for the turkeys to walk over into the new paddock. This worked okay, but it was a pain to move the shelters over the grounded fence and I worried that I would eventually damage my expensive fence. It was also not so easy to get the turkeys to move through the "gate" on their own volition. I ended up needing to incrementally move the back "wall" of the first paddock closer to the "gate," slowly shrinking the paddock until the turkeys felt compelled to move into the second paddock. It was in the awkwardness of this maneuver that it hit on me how to do this much more efficiently.
For the last three weeks I've been using the following method: I start with a super paddock of two fences creating a large circular enclosure. The four turkey shelters are in the middle with feeders hanging protected under the tarped portion. Water is provided by my automatic watering system.