Like this?
I asked earlier what you planned to haul that wagon with. I went this route. Lawn cart from a Farm Implement store but available just about anywhere in several different versions. This one all four sides drop down but I can't see using that option for hauling guns to the range bench or anywhere else you might want to go. Would fit in an SUV with the rear seats down. I haul it in the bed of a pick up. Light enough to lift/load into bed and the inflatable tires make it roll easy.....think it was under $100.....maybe as low as $79 (?). Handles a heavy load pretty well.
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I don't know how many guns, and or thousands of rounds of ammo you carry.Looks like the same ones that garden centers, Home Depot, Sam's and Costco sell; not too sure how well it would hold up with a lot of heavy ammo and such