For example the sweep and knob sketches result in the servo rotating clockwise continuously no matter what changes I make to the code.
That's because you are not using a real servo, but rather you have an ex-servo. Once a servo has been modified for continuous rotation is ceases to be a servo but rather has been morphed into becoming a bidirectional, variable speed, geared motor drive. So while you still need to use the arduino servo software to interface and control your ex-servo, the write values you send to it causes it to do different things then a standard unmodified servo does with the same write values.
This has nothing to do with running sketch code on a arduino board Vs a standalone circuit.