I would make a sprang piece about 6" wide, so the middle section would be 5" or so high (to allow for tapestry draw in).
I can see how difficult it is to needle weave it on the sprang frame. If it's too elastic, I can remove it to a more stable card loom or foam core board, depending. The sprang bits at the top and bottom could be stabilized and left to hang, or be pinned back out of the way.
When it comes to displaying the tapestry, it will hang from a bar at the top of the sprang and one from the bottom. More if necessary to display the sprang bits. Have to see how it acts. Can't have it pulling in the tapestry, but the tapestry might be firm enough to hold the sprang open.