I think there has been a change in the hubs used since Ford went from 16.5" wheels to the current-spec hub-centric 16" wheels. There should be a 16" wheel you can use, but it will not be the same as now used on the E-series, rather a hub-centered 16" wheel for the older 4.88" hub.
It could take some shopping around to find the right dually wheels. Check for wheels that were used on 4x2 F-350 when your E-series was made, or a few years earlier, as they may have been 16" and either lug centered, or at least hub-centered on your hub size. The 4x4 F-350 used more wheel offset, so you might have clearance problems with those.
In one brand, Ford used Accuride 29577 wheels on F-350 4x2, '84-97, and on the dually van '85-91. That one is hub centered and will need the swivel lug nuts.
This upgrade is a little easier on Chevy than Ford, not as much changed in the wheel specifications.