Mustang dies when lights are turned on

Bad grounding. Check all the ground wires. You might need better/newer ones.

Then don't turn the lights on!!!! lol, sorry couldn't resist.

Trace over your wiring, that sounds like your shorting out your distributor to me somewhere when you turn the lights on.
If it just started happening since you swapped alternators chances are your light switch may not be it, but don't rule that out for sure.

I guess one test you could do is pull your #1 plug, ground it with the plug wire attached and have someone turn over your engine WHILE the light switch is on, are you getting a spark?

I'm no expert at this by any means but 100 amps is more than enough
to handle what your running I'd say.

Your one phrase "continues to climb" reffering to your voltage has me wondering whats up especially with a 3G alternator, the fan shouldn't drop it at all, or very little I would think, and then have it "slowly climb back up".

You should get some more helpfull advice by the guys/girls her that are more familiar w/ the 3G problem your having by tomorrow I'd say.

Wiggle the connnections and make sure they're grounding to bare metal and not insulated by the paint.

Does the car die like you shut the key off or does it just idle too low and quit? If its the latter, then maybe that's why you're suspecting the distributor being off a tooth? Any way you can advance the timing a bit more to see what happens?