I like to spend some time really considering ideas like these. Manufacturing these atom by atom would be a tremendous pain, so either the element (or compounds

I like to spend some time really considering ideas like these. Manufacturing these atom by atom would be a tremendous pain, so either the element (or compounds thereof) would have some extremely rewarding properties for its manufacture or one could posit a deposit of something with a reasonably long half-life occurring during the "right kind" of supernova or other highly energetic phenomena -- something rare that might foster competition. The properties of these elements, well, as you climb up the table, you get more and more relativistic effects from these super-heavy nuclei (the electrons end up "moving" -- inasmuch as something can be moving in a QM sense in the electron cloud -- rather quickly), and the elements become more and more metallic. Covalent bonds would "lose" the relativistic effect, and I do not think that many of the compounds themselves would have properties that could not be replicated with something cheaper, but ... there's exactly one area where I do hold out some kind of hope: metastable nuclear isomers. Elements sufficiently far into the island (or even continent) of stability would have many typical modes of decay restricted, and highly-deformed nuclei (some we can find even now are shaped like pears, they are so lopsided), that they might have very restricted methods available to store and release energy. In short, nuclear batteries. We haven't had much luck with those down in the "regular" elements but if I had to come up with a decent sci-fi reason to want many megagrams of MacGuffinonium, the bizarre properties of the nuclei enabling nuclear batteries -- with shocking power densities -- would certainly be eligible at least in a hand-wavy sense.