I have 12v on both side of the ballast resistor with key on and points closed. Could that have anything to do with the starter switch? Or just a sign that I fried it along with whatever else?
I assume the points really are closed and clean and the starter switch is a "12 volt" aftermarket model with a small wire connected to the bypass stud on the side. If so, remove the wire and do your "key on and points closed" test again.
If that gets the coil side of the ballast resistor down to around 9 volts the stomp switch is bad. But that shouldn't keep the engine from running. It would just burn up a set of points faster.
If the coil side of the ballast resistor is still 12 volts either ...
a. the points aren't really closed
b. the wire from the ballast resistor to coil+ is bad
c. somehow the plate the points are mounted on is not grounded
To test that...
a. leave the negative meter lead on ground, the ignition switch on and the points closed
b. remove the distributor cap
c. touch the positive meter lead to coil +
d. if zero volts, fix the wire between coil + and try the whole test again
e. touch the positive meter lead to coil -
f. if zero volts, replace the coil and try the whole test again
g. touch the positive meter lead to the stud on the side of the distributor where the coil - wire attaches
h. if zero volts, replace the coil - to distributor side stud and try the whole test again
i. touch the positive meter lead to point spring where it attaches to the distributor side stud
j. if zero volts, replace the stud and try the whole test again
k. touch the positive meter lead to the plate the points mount on
l. if 12 volts, the distributor is not grounded. If zero volts, OK. Let's worry about this later.