Popping sound in exhaust

The vacuum was attached to a barb at the base of the carb for full manifold vacuum.
Ah OK, makes sense. Certainly sounds like too much advance. If it was on ported vacuum, then disconnecting it would not be expected to change things at idle. So your advance pod sounds like it may be working just fine, just at the wrong time. See if the pod leaks under vacuum; just connect a hose and suck hard on it, or use a manual vacuum pump. You can also watch to see if the advance moves the plate inside the distributor.

And yes, time to break out the timing light!

The rich desposits on the plugs may or may not be connected to this issue.

Check this out it works
How Vacuum Advances Work
FBO Ignitions also recommends full manifold vacuum connection
FBO talks about full manifold vacuum in this type of system in just a few cases, to fix specific issues, not in general.....per that link.

If you look across many mfrs, there are so many variations on vacuum advance and vacuum retard, and pods that have both, it is hard to make generalizations.