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John, there's some discussion on pieces similar to the Headless Horseman
here: http://chessvariants.wikidot.com/attack-fraction 

In the discussion following the chart, Graeme Neatham gives an estimated
value of pieces that move like a K but capture like a Q - 8.45, move like
a Q but capture like a K - 4.50, and a knight-wazir pair with a similar
difference in values. There's also a discussion about why this might be.
Basically, a piece that has a great capture range tends to be more
valuable than one that has a very limited capture range. As long as the
piece can move and position itself to capture, then it is able to fork
widely separated pieces and basically take potshots at pieces across the
board. A piece that can move almost anywhere, but telegraphs its attack by
having to move directly next to its victim, then wait 1 turn before the
capture, is far too susceptible to being killed before it captures. It's
a more limited piece.

Others may well have much better answers. But it seems to me that 7 is a
bit high for that value; yes it has great range, but... 7 would seem to be
a maximum value for the piece.