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David Paulowich:
| When the King and Rook are widely separated, the winning move in this
| endgame involves moving the Queen 'x' squares, checking the King ('y'
| squares away) and attacking the Rook ('z' squares away). Usually at
| least one of x, y, z is greater than four, which suggests that the
| Short Queen would not win against the Rook in an endgame with only 
| four pieces on the board.

Your conclusion is correct: King + halfling Queen vs King + Rook is in
general a draw. Only 3.8% of the btm positions are won to white, and 40% of
those because black is already checkmated. There are a few lengthy mates,
though (where the black King starts trapped in a corner), the longest
taking 44 moves to mate or Rook capture.

I am not sure if this suppresses the value of the halfling Queen as much
as you think, though. KQKR end games are not that common. I play-tested
the 'Quareter Queen' (FWAD, which I believe is also known as Mastodon),
and in end-games with only King and Pawns as other pieces, it seemed te
Mastodon  was very close to being exactly halfway between R and Q. I would
expect the halfling Q to be better than halfway between Mastodon and
Queen.

Commoner was only slightly stronger than Knight, perhaps a quarter Pawn,
in endgames of two Knights against two Commoners in the presence of King
and (many) Pawns. So I got the end-game values

Knight   = 325 (Kaufman)
Commoner = 350
Rook     = 500 (Kaufman)
Mastodon = 750
Queen    = 975 (Kaufman)

and, based on this, would estimate the Halfling Queen somewhere around
875-900.