This design uses M8 threaded rod to be easy to adjust (sorry, I'm not configent in using imperial hardware). While the tips and the back screw directly onto the rod I made an inset in the top part to accept a M8 (locking) nut to prevent the thin part from accidentaly turning.
Once the distance between the back and the front part ist set up it can pivit arount the upper edge of the wood piece in the front. The hook on the back will prevent the front part from falling into the room.
The hooks itself are designed to not interfere with standard sized spools (I've referenced the 200mm spools i had on hand).
With a different lengh of rod on the tips the holder can be set up for singel or dual spool usage. Feel free to use threaded or smooth rod. If necessary even bearings could be installed on this shaft but i think it will work just fine and be much less complicated when changing the spool(s).
If larger spools require more room the two longer rods can be swapped with even longer ones.