Carolyn, you have some great answers -- the important thing to remember if you home-freeze melons is to eat them frozen -- not like rocks, but like cold ice cream -- I don't think there's any way that you can home freeze melons that doesn't result in a limp product if they're allowed to fully thaw -- but they're good eaten still frozen.
The sugar may be intended to remove some of the melon's liquid, rather than to season or preserve the melon pieces that you intend to freeze.
I've used salt to reduce liquid when freezing pieces of summer squash or eggplant with reasonable success. Success in the sense that they don't lose all their body and can be used a little more effectively in cooking -- or in fixing slices to pan fry, but again, I use them while still mostly frozen.
It might be that you could sugar the melons and let them stand a bit, then rinse, drain and freeze . . . and still eat them frozen but largely unsweetened. Or you could salt, rinse, drain as I do with the summer squash.
If I was doing that, and lacking the liquid nitrogen Worth suggested, I'd freeze the pieces on a tray to get them frozen as fast as possible, then package them.
The other avenue is to mix them with something. Smoothies were mentioned, but there are probably other ways you could mix them with just a little of something you like and freeze individual portions in liquid or semi-solid form.
Anything that is 'touchy' about being frozen I freeze in individual size ready to use amounts. My most common method these days is to put one of the cheap fold top plastic sandwich bags inside a round plastic cup that formerly contained cream cheese or yogurt or something of that sort, freeze, then remove, fasten the top of the bag tightly to exclude air, and put the one portion bags together in some larger bag or box for freezer storage.
Again, though, however you process them, the way to have 'pieces' of frozen melon to eat that taste like melon, is to eat them frozen, just thawed enough to enable you to get them down.
If you do some web prowling for info on 'how to freeze melons' you'll probably find some other good ideas. If I get a chance later I'll look in some of my old cookbooks and see if there are any inspiring suggestions -- but freezing melons is something I formerly wanted to do, so I think the above probably covers most of the suggestions I found.
Another possibility is to research ways to keep melons an optimum time, and just eat them as fast as you can, compatible with keeping your innards properly working.
If you find a great way to freeze melons, please blow trumpets and post it, as I bet there are many of us who've looked for one.
