I did not have any ignition issues when I converted my 51 to 12 negative ground. But I do run an electrical fuel pump either. Since I don't know what pump you are running I can't say whether it's a wiring issue or the pump isn't compatible with negative ground. Regardless, a 6v fuel pump will probably need changed to one designed to run on 12v.
I used the alternator and regulator setup from an 87 Dodge Diplomat, here's how I mounted the alternator.
http://www.yourolddad.com/12-volt-conversion
You will need 12v bulbs, they do not care about polarity. Unless you are running LEDs.
The heater fan needed addressed, my old one was falling apart so I found a 122 one that worked fine.
http://www.yourolddad.com/blower-motor
Wipers were an issue, not sure if those gold resistors work well or not. I built a current limiter to handle that for me.
My ignition is stock 51 Plymouth EXCEPT for the coil, ballast resistor and the starter relay. I used the coil and ballast resistor from a later model 12v MoPar, such as my 65 Cuda. I mimicked the ignition system of a 12v points type mopar like my 65 Cuda. In this setup 12v, in run, goes to one side of the ballast resistor and the other side goes to the coil positive terminal. In start 12v needs to be fed directly to the positive terminal of the coil. If you use the relay I linked it has a 4th terminal, labeled I that provides 12vv when in start, run a wire from there to ether the coil positive terminal or the coil side of the ballast connection. If you use a coil that does not need a ballast resistor, like your link, then ignore any ballast mention in my write up.