Okay, Negative Nelly...Don't cloud my head with facts.

I've been mulling this over thru the night.
You don't really need a remote mounted full hydraulic planetary overdrive, we're not talking thundering horsepower and pulling fifth-wheel trailers here. Just a simple gear-splitter will do. It'll take some fancy machine work with an engineering guy to work out the gears, but here's my thought. It doesn't have to be big and heavy; the case can be aluminum and mounted right to the diff, and may even be thin enough we can use the existing driveshaft.
Here's my cocktail-napkin sketch to show what I mean. Nothing's to scale and everything's exaggerated, but hopefully it'll get the idea across.
The driveshaft and diff are offset slightly, and terminate in bevel gears. A selector arm holds two idler gears: one idler gear in mesh with both main gears at their common tangent, or a stepped idler that meshes with both main gears at some other point of their circumference.
Top-right sketch shows direct drive: the stepped idler makes up the difference between the main gears' sizes, and results in 1:1.
Clutch in, push the overdrive lever, and a rod rocks the selector arm, as in the top-left sketch. The single-size idler runs both main gears, the difference in sizes resulting in an overdrive reduction.
Bottom sketch is sort of an overhead view: diff to the left, driveshaft yoke on the right, bearing and case shown, and the rough arrangement of the bevel gears.
It would have to bolt very firmly to the diff, and may need some jiggery-pokery to use a gear in place of a diff yoke...but with some engineering geniusry, why couldn't this work? The gears would be at least as robust as those in the tranny. Few moving parts, light weight, easy to produce = profit for someone!
No synchros or anything: downshifting should be an easy matter of clutching in, and easing the gear in while the revs fall. Upshifting may be best done while you're stopped, but once you're in OD there'd be no reason to get out; as 3rd would be 4th, 2nd would be 3rd, etc.