Robert, you were looking for an easy way to frame the layerscape ... you might consider basket reed. You can purchase reed from 1/4" through 1 1/2" wide at
www.basketpatterns.com And they also carry basket strips of ash, walnut, maple and birch which start in the 2" wide range.
One pound of reed, which lasts forever, runs between $6 and $9 per bundle.
Reed is very easy to use. Once the stack is assembled and the glue dry you cut a strip of reed about three times the outside dimensions of the work. Reed can come is very long lengths inside the bundle.
Soak the reed in cool water for about 1 minute and it becomes extremely flexible. You can tack one end to the outside edge, wrap along the outside dimension, it folds easily, and then when you reach the other end do a second tacking.
It's easy and it's very very cheap when you want a neat looking end but little or no cost to framing .... rather spend the saved money on More Wood!
OOOOPS, forgot, there are some great water dyes that you can purchase for basket reed or use power wood dyes to add some color to your wrap frame.
Susan