I thought about how long it would take to stitch all those scraps of sheepskin into a piece big enough to serve as a top flap, and grabbed another sheepskin instead. (That makes $90 in materials for anyone playing along at home.)
It's pretty well stitched together. I tried a sort of flat overcast stitch to butt the edges of the flap and the bag top together. I might go and stitch the flap into a sort of a cap (it goes up and over the top of the lyre, which sticks out of the bag) but I'm not sure about that just yet.
The lyre fits in, but it's really snug. Like "push the bridge down to the tailpiece and get wool stuck in the notches" snug. I am considering going through and giving the fleeces all a haircut, to open up some space inside the bag. But I'm going to sleep on it - I can't put it back once it's cut, after all.