Ok, let's try the carbs.
No pulsing without the alternator. My current theory is that the alternator has been the problem all along, but when I previously disconnected it, the engine still ran poorly because the plugs were gummed up. That may have led me to incorrectly rule it out as the source of the problem.
I drove the car around a bit tonight with no alternator, and things seem to be improving. I'm picking up a new alternator tomorrow and hoping for the best.
-Scott
It was the alternator after all. No more pulsing lights... and the car runs perfectly. Thanks for all the input!
-Scott