Well I gave it a go today, here's what I did.
I bought a block of beeswax at Michael's Craft Store.
It's a two pound block which cost me $20, but I think it'll last for quite a few restorations, if not the rest of my life. I chipped some wax off of the block with a screwdriver. Then to melt the wax I used what my wife calls a tart toaster. I just loaded all the chips into one section on the "toaster." You can see the fragrant wax in the background there. I had thought about using that wax, but I didn't want all of my TVs to smell like blueberry cobbler.
I removed the old cap from the set and removed the wax from the exterior and the old capacitor from the interior. I used hot glue to seal the new capacitor inside the old cardboard form. Then I gave the whole thing a quick dunk into the beeswax. Here's the result.
It still looked a bit off to me so I used the paper towel that I wiped the old dirty wax off of the cap in the beginning and I "buffed" the newly dipped cap with it. Here is a picture of three finished re-installed caps.
They aren't quite perfect yet, but I'm hopping that after a dozen or so more I'll make them indiscernible from the originals.