Snaps may do the trick. I've considered zippers or Velcro too. Most of the issues are trying to eliminate gaps at the ends and the current designs get into all kinds of drawstrings and bungee cords. Velcro or zippers on the ends would seal better.
My dream setup would be an an asymmetrical hammock with an integral zippered side-entry bug net, just like a Hennessy. There would be a quilt sewn to the bottom in an asymmetrical pattern, with a good overlap for the user-- no point in going all the way to the ends, IMHO. The entry side of the quilt would have a 2'-3' zipper, so you could add more insulation like a small quilt or foam pad. You could make that quilt insert wearable for a camp puffy, like a vest or serape. You could still mount a regular underquilt for colder weather, or have a full length underquilt and integrated top cover for colder winter camping, with the top cover aiding the support of the second outer underquilt.
Clark hammocks have an interesting approach to the issue, with pockets sewn to the underside and accessory bats, like pillows that stuff into the pockets (Z-liner system). There are triangular bats that cover the ends. There is a fellow with a Youtube video that shows off the features on a Clark: http://www.youtube.com/watch?v=uaGZHrKrK50
I think the Clark makes a good illustration of how the camping hammock market has developed. It started out with basic gathered end hammocks and continued to more complex designs like the Warbonnet Blackbird and the Clark. My assumption is that the cottage hammock makers were more oriented to the main hammock and suspension components and not as interested, skilled or tooled for making baffled quilts and the rest. Clark has a fully integrated system of hammock tarp and insulation, but a North American model plus Z-liner is going to set you back about $550. A Hennessy will run $170-$240 for a hammock and tarp, but you still need to add insulation and that is buried on another page and you can add another $150 so the total is more like $320-$390. And Hennessy says the SuperShelter is a 4-season package, but there's no way you're going below freezing with it.
So the market is really a piecemeal arrangement of hammocks, tarps, quilts and suspension. Jacks R Better has bravely taken the issue on by offering a complete hammock camping package--- to the tune of $799 and I think that is why many other makers haven't gone there: the price of a real coordinated system in one gulp scares people off. Of course many already have a tent, sleeping bag and pad and they may have paid more than very nice hammock system, but they got there piece by piece in an evolutionary kind of process. I think it rarer for someone to go out and buy a spendy tent pad and bag all in one gulp. So dropping another $800 for the privilege of sleeping 18" off the ground is daunting, but you're going to end up going there anyway if you want to use a hammock north or south of the Tropics.
So some poor sap buys something like a $20 Grand Trunk Ultralight thinking that can go camping with it. They then proceed to nickel and dime themselves, buying workable suspension, bottom insulation, tarp, bug net, etc, etc. KA-CHING, KA-CHING!!! Surprise, surprise, surprise: the hammock body is the cheapest part of the deal. And not one major hammock manufacturer will tell you up front that you can't do squat with a plain hammock body below 60F. Walk into REI and you'll see Hennessy or ENO hammocks, but nothing else to go with them. I don't think it is a scam or conspiracy, but it is a little messy. Even the ultralighters have found out that their existing 20" wide pads aren't useful, nor are most of the tarps out there, unless you have something bigger than 10' on one dimension. Ooops!
Now where we're all done with it and we're ready to put up our hammock. Wrap the tree straps, attach with carabiner or toggles, set out a couple stakes and guylines if you have an asymmetrical model, get the tarp hung to the trees and and 2-4 more guylines and stakes, and hang your underquilt with yet more suspension lines and associated hardware. Add a bug net of you don't have a hammock with an integrated one. Then you can get in with your sleeping bag or quilt and tweak the underquilt into place, hoping it doesn't gap at the ends or shift as you move during the night. I think that is sloppy, especially on the underquilt part and I think the designers and makers can do a better job. SOMEBODY needs to find the fortitude to offer a hammock suitable for 3 seasons in North America that doesn't look like a backyard laundry line!