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Either Shogi - the drops along with the slow moving generals make this a
very gradual game, yet with plenty of exciting attacks - or Chu Shogi - a
complex Shogi variant without drops, but lots of interesting pieces and
very rich.

I could see myself playing either of those for a very long time without
becoming bored... (as long as the hypothetical desert island includes an
opponent of a suitable level).

Or, if it has to be a variant of western chess, I quite enjoy Parker's
Dragon Chess (not to be confused with Gygax's) - it is very close to
normal chess, yet different enough to feel like it offers more
opportunities, and unlike the various variants adding Capa compounds, the
dragons aren't overly powerful.

Perhaps for sheer variety, Navia Dratp would be a good option - 44
different pieces, and build your own army, allows for a lot of
possibilities.

Of course, given that one of the things I enjoy about chess variants is the
sheer variety - encountering new ideas, having to think in slightly (or
radically) different patterns - being restricted to just one variant, no
matter how good, would be dull compared with exploring the richness of all
the weird and wondrous variants people have invented.