I guess I wonder if MOS schottky techniques would do anything employed on Ge, or SiGe for that matter. (On that note, there are some SiGe schottky out there, with incrementally better specs; SiGe is a fairly simple process as things go, AFAIK, so it's not as scary as it sounds.) Mostly, or pure, Ge, the Eg is probably just too low to get reasonable temperature range, even with improvements like MOS.
Likewise SiC should be extendable into the some-kV range at good performance, good enough to still be limited by bulk resistivity; not that we'll see (or, frankly (or hopefully?!) need?) it in consumer-industrial applications, but distribution-level and high-power converter or generator applications can benefit.
Tim