What depth are those, "shallow's"? If they're 5-11/16" and didn't come with frames you could cut some strips and add a rim 1-1/16" to bring them up to medium size, 6-5/8" and then use the appropriate frame size, 6-1/4".
If they are 5-11/16" shallow supers, I envy you, I still am uncomfortable lifting medium supers full of honey. If I had 50 or more shallow supers I'd be even happier to shift my operation to the even shallower supers.
You could use all-shallow supers, 4 for the brood chamber and however many more, as necessary, above those for honey storage. It should be even easier with less weight.
And the more I think about it the better I like the idea of, 8 frame - 5-11/16" deep supers.