That parts interchange manual/site is called "Hollander" or that's what I recall.
The problem is that in 1983 and earlier, E350 used "lug centered, COINED" wheels. Look at one of your wheels. You'll see four holes are "countersunk" and the alternate four are "upset" or "raised" on their edges. That's why there's a hole I the wheels for the locating pin (on rear hub only) to align "upset" and "countersunk" so they mate. Then the lug nuts cam into the holes and center the wheels.
This is one of the toughest wheel swaps. I looked at it in 2000 and just bought 8.75R16.5 replacements. Jose (DaHose) tried a year or so ago and bounced off the problem too. Got Firestone TransForce 8.75R16.5's also.
They have to be Lug-Centered, Coined, and have the right Bolt Circle Diameter. They ALSO have to have the right OFFSET for the 16" tire size you want to run. My guess would be 215/85R16 or 225/75R16.
One of the most helpful references is
Barry's Tire Tech, which is published by a member here, CapriRacer.
I think it's been done, but it can be tough to do. You may want to see who used coined wheels but went to 16" tires earlier than Ford did. Nobody's using them now. If you have 8.00/16.5 and not the clearance for 8.75R16.5, that's another issue. With the Ford chassis, I think you're OK with the 8.75R16.5 that's still being made in TransForce. The 8.00 is not.