I would give the 22g a try for a banana style patchbox. Normally I would use thicker, 18 to 16g like Angus suggested, but since you will not be trying to form compound curves around a buttstock like you would with a conventional 4 piece patchbox, I think you could pull it off. You have nothing to lose since you already have the material. Between the hinge and a few gentle curves in the lid, I think strength will not be a problem and besides that, the thinner material is easier to work.
David