I really like your alternative to panniers...especially the homemade security covers! My wife has a pair of Wald folding baskets mounted to a Delta rack and it doesn't wobble at all.

Did you make the baskets themselves or buy them? They really look oversized lengthwise and might hang too far in back of your axle, causing your swaying problem. You can try to scoot them forward if you don't have a problem with heelstrike.

I'm not sure what kind of rack that is, but it looks mightly long. This might also compound your problem if it is not rigid enough (a Jandd Expedition rack is long and rigid). Try holding the back of the rack and pushing it side to side...it should barely flex if at all.