I have a 1/6hp split phase induction motor 1725rpm, and the wiring panel has
tabs onto which wires are connected via 90deg crimped-on terminal
sockets. ...
Some questions I have a
- one of the starter winding wires (red, black) is too short to reach
the other tab to reverse the rotation direction - is this normal or
should I pull on them harder?

Rotation direction isn't always reversible (some motors, you would
reverse
the motor and use the shaft on the other end of the motor). If it IS
reversible,
you MUST let it spin down to a stop so as to re-engage the centrifugal
switch
before attempting to reverse

- how would you normally attach a DPDT switch to reverse the rotation -
do you cut off the sockets and splice on another wire to extend outside
the panel? do you use the existing socket on the wire and plug in your
extension wire?

I'd worry about wire-stuffing limits and heat rating of the terminals
(the motor
can get warm). If possible, you should put all wires from the outside
of the
motor into bolted-down attachment points (so they don't tug directly on
any
of the motor winding wires), and there are often 'spare' attachment
points
in the motor for this kind of addon. There are 'feedthrough' crimp
connectors
that both accept the wire terminal AND plug down onto a bolted
terminal,
for just such wiring issues. Because you have to stop before
reversing,
reverse switches are usually forward/brake(off)/reverse three way
paddles. The 'brake' means there's a resistor or short across the
motor
windings in the off position, to spin it down more rapidly.

Reversing switches are only common on three-phase motors.

- where would I ground the motor? I don't see any specific
tab/terminal/screw in the panel or on the case for the grounding
connection
Keep looking; sometimes a nut is painted green.
Sometimes you use the screw that closes the wiring door.