One of the wee elasticated covers you get for kerbside recycling boxes would be good for a basket/box, as long as it had a lip.
A few years ago I picked up a few spare Vaude pannier-hooks, with the intention of one day owning a second pannier which I could then adapt in the same way as my first (with a bit of wood inside, attached to the hook, to keep the aft end clear of the spokes and with a pair of Vaude QMR hooks on the top rail to replace the original non-locking hooks), but in the meantime I've since looked at them speculatively with regard to potentially using them to help a basket attach to a rack in a quickly-releasable way.