If your main goal is just to incorporate "hit-and-run" attacks, you could
put them on a less powerful piece. For the Crown also has a piece called
the Charger that moves as a R3 but can "overrun" an enemy piece and
continue moving up to its maximum range (and even capture multiple pieces
in a row). I've seen a couple of other variants with similar pieces.
I estimated its value in a FIDE context as ~6 pawns, but that hasn't been
tested and might be far off. If you happened to produce any new
information on its value, I'd be interested.
(Trivia: The last expansion for For the Crown originally had another unit
called the Behemoth with the same "overrun" mechanic, but on a Q3 instead
of a R3. It got scrapped because it made it too easy to obtain a perpetual
check.)
