The short is likely at where the spade lug connects to the terminal stud on the arm of the points. When you install the lug you have to bend it at a 90 degree angle so that it will clear the side of the housing so that when you operate the spark handle, and the lug rotates, it clears everything.
The wire that connects the two plates is also a special wire (Bratton's carries them) that is multi-strand and very flexible. Many "restored" distributors have an incorrect wire in place and it creates problems such as you are experiencing. The wire needs to be very flexible so it can withstand the constant movement caused by the spark handle. When I rebuild a distributor I also add a large thin insulated washer under the stud of the arm of the points to further ensure it does not short out.
My suggestion is that you correctly rework the distributor you have and leave it as Henry designed it. The modern stuff may work ok, but it doesn't really add anything and it could just create more problems for you.
The area where you live, Temecula, has an abundance of Model A folks. If you are not a member of the Palomar Model A club, you should consider joining. One of those folks could have your car running in no time.
Tom Endy