Thanks for the suggestions. I've used ziploc bags for years, but end up with a jumble of them in the bottom! And I did get a set of packing cubes, but planned to use them in my suitcase.
In the meantime, I've found two useful items:
(1) A SwissGear-brand "vertical travel bag" from Target. Although the specs give it as 7.3 x 6.3 x 3.1 inches, it seems bigger. It has two main compartments which can be opened up almost fully, and a bunch of other compartments and pockets. It does not have a flap, which is important if it's to be used inside a larger bag. It's quite light-weight.
(2) Also at Target, on clearance, a really cheaply-made lunch box/bag ostensibly insulated with that metallic stuff. I wouldn't bet on its holding up very long as a lunch container, but as a packing "cube", I think it will be good. (Unless that metallic insulation is a problem at airport security. Anybody know?)