I have a mosquito hammock that I use in cool weather upside down with the netting holding the underquilt. Just set the hammock up right side up (there is no ridgeline), lay the quilt in it, zip the netting closed and flip the hammock. Sometimes you have to make sure the quilt is spread out after the flip but it stays in place well. The netting pulls fairly tight but does not compress the quilt but it is a thick quilt (RayWay alpine) so it tends to take up a good bit of space.
Someone mentioned one drawback of this - the netting catches on things easily and picks up leaves and dirt if it touches the ground so you need to use a little care when taking the hammock down if you leave the quilt in. I now leave the quilt in and use a Bishop Bag with good results. I am in the process of making an underquilt for this hammock that will have regular suspension so we can use the bug net as a bug net now that the weather is warming up.