I don't think anyone pointed out the width issue in plain language. A pad underneath helps with CBS but you also need some side insulation. A wide pad like Gossamer Gear sells or a SPE like Shug pictured puts some insulation up where your shoulders/arms/knees can come in contact with the sides of he hammock. They are at the same temperature as the surrounding air. Down collapses under pressure and you get a cold spot.
Quits address it by being wide enough to insulate the cold spots on the outside.
Pads need to be wide enough to wrap around your shoulders and maybe your knees. The easy low cost way is to cross two CCF pads between the layers. They can be cut to lengths that suite. Increasing in price is the wide pads than the SPE. OTOH the SPE lets one use smaller pads that are easier to handle.
The relatively low compressibility of CCF makes it easy to use between layers that also more or less hold it in place. That will not work as well with an air pad but you can put that inside.
I'd start with two CCF pads. The better one's have smaller pores if there is a choice. They are softer to fold around you but still do not compress much. ;-)
Free advice worth what you paid for it. ;-)