I'm trying to find a style that can generate piano accompaniment in the style of George Shearing.
Tech support suggests using the Familiar Song search in the StylePicker, but this merely generates a list of 100 styles, none of which mention George.
Does anybody know?

Welcome to the Forums.
Don't know if this is helpful but thought I'd share that I recently had a different kind of George Shearing challenge:
I was looking for an acoustic piano Melodist for a song I was writing in which I was using the _BOND.STY style which includes an Electric Piano as part of the style.
I selected Melodist #66 Slow Swing Shearing, with a Harmony of 16 Shearing Piano, unchecked Allow Style Change and cleared the Use Real Styles box. Generated the melody and lo and behold the results gave me that Shearing sound and feel I was looking for:
Lost In The Groove

There are some older styles, including -J_NOPNO, but I would search for styles which more closely match Shearings's classic deliveries. Try these:

_STREET

_NOIR

_JAZVIBS

_SECLUSE

_EOS

any of these might all work.