As for me... I followed through on the suggestion from
Jim 68cuda's advice and, instead of the elaborate 'leaf spring' set-up I started this thread by proposing, simply spread on the lightweight DAP spackling at the beginning of the grade, feathering it out about 6-8 inches.
There was a bit of a learning curve to using it. One trick is that after initially putting a glop of stuff on, I needed to trowel it very very *lightly* so as to get a natural, feathered grade down to the foam baseboard. Too much pressure and you end up just wiping half the stuff away! The other trick is, although the spackle's made so you can paint over it within an hour, if you're sanding it YOU MUST let it dry and cure for at least 18 hours and more likely 24 or more.
Here's what it looked like -- I'll admit the picture looks pretty rough, but it's quite smooth and even to the touch, and moreover, with cork on it, any imperfections seem to be completely eliminated.