Interesting. It looks like the F350 4x4's or DRW's didn't come with hub caps.
The snippet from the Master Parts Catalog, below, doesn't even give a part number. (1130 is the base part number for hub caps for any Ford vehicle anywhere in the world.)
And the 1984 Truck Facts Book, which Ford supplied to the dealers, says in the Standard Trim Features section: Hub Caps - Bright. Not available with F250 4x4 SuperCab, F350 4x4, F350 Dual Rear Wheel Models or F250 4x4 models with heavy-duty front suspension."
As for your measurement, Big Blue's D60 hubs measure about 4 1/4" in diameter. So you apparently have the "heavy duty front suspension".
Gary, AKA "Gary fellow":
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Dad's: '81 F150 Ranger XLT 4x4: Down for restomod: Full-roller "stroked 351M" w/Trick Flow heads & intake, EEC-V SEFI/E4OD/3.50 gears w/Kevlar clutches
Blue: 2015 F150 Platinum 4x4 SuperCrew wearing Blue Jeans & sporting a 3.5L EB & Max Tow
Big Blue: 1985 F250HD 4x4: 460/ZF5/3.55's, D60 w/Ox locker & 10.25 Sterling/Trutrac, Blue Top & Borgeson, & EEC-V MAF/SEFI