RE: Where did I go wrong?
What you did is impossible with any servo that I'm aware of. Put the wires back where they started. You may or may not have ruined it. You could have shorted your receiver in the worst case. You have a few options:
First, obviously, get a radio that works. This will be the most expensive option. However, if the reversing switch is broke on the radio, what else is broke? Is it even safe to use?
Second, get a reversing Y for about 10 bucks, and hook the servo up to the reversed side of the Y.
Third, get a matchbox for about 70 bucks.
Fourth, hook the pushrod up to the other side of the servo--may or may not be possible
Fifth, get another brand of servo that operates in the opposite direction.
Sixth, set up a series of bell cranks that would reverse the travel of your output.
There are more options, use your imagination and modeling skills. I assume you have some modeling skills, since you know how to go "old school."