Thanks for sharing your observations and experiments. This is a valuable thread. It may save others a lot of work, and it might also inspire someone to come up with yet another solution.
You asked whether you'd feel the bungee loops under you, and I don't know, because mine are sewn to the bottom layer of an insulated hammock, not to the hammock bed itself. Also, your idea of velcro tabs might work, but you'd lose the elasticity of the bungees. Hammocks stretch and change shape as we move in them, so locating places to attach a supplementary UQ will always be approximations. The stretch of the bungees compensates for minor misalignments. I experimented with magnets to hold the layers together and found that even very strong magnets have far less shear strength than peel strength, so they slide apart. (I'm still working on a solution that will compensate for that.)
Lastly, FWIW, here's my method of making an underquilt that fits a hammock because it's the same shape as the hammock when someone is lying in it. (Warning #1! This is labor-intensive verging on obsessive.) 1. Have someone the right size lie in the hammock. 2. Draw triangles on the bottom of the hammock, covering the entire surface. 3. Measure each side of each triangle. 4. Use the measurements to make tyvek or paper triangles. 5. Tape the triangles together in groups, so each group forms a flat pattern piece. 6. Use the pattern pieces to cut out fabric pieces. (Warning #2! So far it has just been tedious; now it gets tricky.) 7. Sew insulation to the fabric pieces. 8. Assemble the pieces to form the curved top layer of the UQ. 9. Scale up the pattern to use for the bottom layer of the UQ. (Trickier still.) 10. Attach to hammock. (Tricky, trick, tricky .... You get the picture.) Don't do this, even though it works.