<Just what is the proper way to ground the exhaust?>
Buy tinned metal "ground braid", this is woven mesh like a coax shield but flattened and fully tinned so it won't rot out under the car. You can also buy it as battery ground in 1-2' lengths and use them. Secure to the exhaust with stainless pipe clamps, and use NeverSeize or another anti-corrosion paste between the metals to ensure good conductivity and prevent corrosion. The ground braid if flexible, that's the key. Ground the tailpipe, maybe one in the middle. Check the engine grounds, there are usually several made of the same stuff, i.e. on the transmission, from the engine to the firewall, and one bypassing a motor mount.
<Would wrapping the wire harness with "metal" tape work? Would the tape need to be grounded? > What harness do you mean? Metal tape can shield and yes you'd have to ground it, usually at both ends. Coax shield is often used for this, or metal shield sold to protect hydraulic lines. If you get a "mobile ham" book up into the 70's they still show basically shielding everything in the car in order to try containing the noise.<G> Might be a lot of unnecessary or futile work.
<a '97 Ford F-150 that belongs to my employer,> I think there are some posts about the F150 in the "mobile" section, and Ford certainly should have some information for you. If the dealer says "Duh?" call Ford directly. Since the truck belongs to your employer...the less modding you do the happier he'll be.<G>