Does anybody know of a travel box where I can keep my 1# screw/nail boxes in their original cardboard box. Or, plastic bins that will allow me to neatly stack my original boxes and slide the plastic bin back onto a shelf?

How many boxes do you have?

I would look at Akro Mills or Milwaukee Packout wall.

Milwaukee

Akro

Harbor Freight has a whole bunch of boxes too.

Would Plastic polymer ammo cans link work for your needs? There are many options and sizes available out there.
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Looks like Akro or Harbor Freight might work. I won’t be able to keep anything in the original cardboard boxes but it might work.

Don’t ignore tackle boxes. Might find a fit there.

I went with the Harbor Freight cases. Thanks