[DonRotolo]

When placing a limit switch, one must not use it as a hard stop; that is, it shouldn't be in the way of the arm and get damaged if the motor spins too much.

Instead, you position the lever of the switch so that it gets touched by the side of the arm as the arm passes by. That way, if the arm goes too far, the switch is not damaged at all.

Another comment: Idea #3, using just time to set a position, will lose accuracy significantly over the course of a match. Variables (such as system voltage) will make this a very inaccurate method.

If I were doing this, I'd use 2 limit switches - one for "frisbee launched, return to starting position' and one for 'arm in starting position'. Easy to program, inexpensive, and more than accurate enough.