Bypassing ballast resistor

aka,
The diagram you posted in post #25 is correct & that is how you should wire up the new system.
No ballast resistor. The only thing that might confuse people is in the diagram it states the old coil [+] wire now goes to terminal 85 on the relay. Two things to note about this: there could be more than one wire that connected to the coil [+] terminal. ALL of these wires need to connect to terminal 85. There might be a condenser connected to the coil [+] terminal. Remove it, not needed.
Thank you hopefully I can get this started