Geez, I don't know how that post got in twice.

Yes I just run the woodpecker over the bottom covering. Whether it's over wood structure or open structure doesn't make any difference. Then I just iron on the top covering. I've tried a lot of techniques and this works best for me. It's not real good with transparent covering because you can see the pecker tracks through the covering.
I do try to avoid doing this over solid structure though when I build the plane. In that case I cut all the patterns out and lay them on bare wood, woodpeckered. But if it's a previously covered plane and I just want to change it I just go at it with the woodpecker.