An under quilt is the way to go in a hammock. It hangs under the hammock.
You will find that many/most UL backpackers don’t use sleeping bags these days, at least until well below freezing. Insulation needs to lift in order to keep you warm so that part of a sleeping bag isn’t particularly effective at keeping you warm. This holds true for sleeping on the ground or hanging in a hammock. Quilts are particularly nice in a hammock where it can be quite awkward to get into a bag.
Pads in hammocks have problems. They aren’t wide enough to wrap around your shoulders and they can be difficult to stay on top of. An underquilt will wrap nicely around you and stays lofted.
You should poke around Shug’s YouTube channel. Look at his playlists, particularly the noobs one and the insulation series. While there, you might enjoy seeing his thoughts on boiling water because they are quite funny (at least to me). https://www.youtube.com/user/shugemery