Very late to this thread, but I just did this portion of Jennifer Moore's double-weave sampler. Here's the process I used to get through it. It was slow-going, but this system made it a little more efficient.
1. LIFT SHED (ONE HALF) OF ACCENT COLOR

* Put a piece of paper under the shed to more clearly see the strands to count out the counted design.
* Use a pick-up stick (PUS) to pick-up the threads based on the chart.
* Remove the paper.
* Turn PUS on its side to raise shed more.
* Slide double-pointed needle (DPN) in between shed behind the reed.
* Release treadle.
* Remove PUS at fell line (in front of reed).
2. LIFT SHED (ONE HALF) OF BACKGROUND COLOR
* Use PUS to place in between layers, making sure to not pick-up extra accent threads. (I had to manually pull up on the shaft to get a shed.) Only one-half of the background layer and picked-up accent threads should be on top of the PUS, which is currently at fell line.
* Turn PUS on its side to create the shed.
* Release treadle and pass the shuttle through the manually created shed.
* Remove PUS and beat.
* Remove DPN from behind the reed.
3. REPEAT STEP #2 FOR THE NEXT SHED (OTHER HALF) OF BACKGROUND COLOR
4. COMPLETE THE SEQUENCE BY THROWING THE PICKS THAT FORM THE BACK OF THE CLOTH
Hopefully this helps someone else!