Do I really need the wire from the alternator to the bulkhead connector?

If you want the factory ammeter to work, then yes, you need it. If not, then you can run a large gauge wire (forgive me I cannot remember the correct size) from the alternator to the large stud on the starter relay. This will effectively render the ammeter useless, as it will not read correctly any longer.

I've thought about doing it to my car, but everything behind the cluster is in good shape and I have no melted connectors anywhere. THe only things I have added electrically are the electronig ignition and a decent stereo system....although it has no external amp, so no big draw there. My ammeter works great and all the wiring is in good condition. So I don't plan on modifying anything at this point.

Thanks Rusty. Adding that wire is exactly what I did when I put in the EFI to begin with. I figured a constantly running electric fuel pump was never part of Ma Mopar's plan, and it would put too much stress on the bulkhead connector and ammeter. Of course the ammeter no longer does ammeter things, but I'm OK with that and just run a volt meter.

Before EFI I had the exact same setup as you; just a simple stereo and electronic ignition, no melted wires and everything in good condition.