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

I am no pro in auto or electrical; and I too, am going on my own journey with wiring.
That being said, make sure you have a safety in place from your new alt wire. A worst case scenario sort of thing; fuse/breaker/fuseable link. The latter may or may not have been with your original harness.
Ive done something similar on a valiant as what youve described youre going for, and the only real obstacle immidiately I noticed was making sure clean/new power goes to the goodies that used to be spliced off of the ammeter wire [wether you used it, kept it, changed it etc].
I believe I'm understanding your question and yes, isolating that wire the way you're thinking from your 'new power setup' and send a live 12v into the old 10awg/"P" connection on the bulkhead would work the way you're thinking.
Better? A matter of opinion.
I ended up doing the same as I worked through cleaning things up and inspecting on my dart; that I had already unhooked the factory ammeter in.
Just my 2cents