Beading has so overtaken me, that last month when I was teaching two hand quilting classes for Capital Quilters Guild in Raleigh, I realized just how long it's been since I've hand quilted!
Years ago I solved the problem of securing quilts into a frame/hoop without damaging the beadwork - or other embellishments added to the piece. (FYI: I always use a 11" x 17" QSnap frame when hand quilting).
Notice the clip on the left holds the quilt to the framework without interfering with the beadwork. Yet, on the other 3 sides, I wasn't able to use clips because they'd be positioned over the beading. Instead, I pin or thread baste the quilt to a muslin sleeve that's attached to the framework.
Make a fabric sleeve the desired length....kinda like making a (elastic) casing for a skirt, with a 1-2" extension. Disassemble the QSnap frame enough to slide it in place.....you will pin your quilt to this sleeve to hold it in place....rather than using the clips. Obviously, you can make one for each side if necessary.
Here you can see the quilt positioned onto the frame and pinned to the sleeve.
Another option I use at times is to simply wrap the excess edge of the quilt around the frame and pin those two layers together as I've done above. When only quilting a little bit in an area, this is a fast way to secure embellished work into a frame. (rather than attaching a sleeve and pinning to it.)