Seems like the bottom line is the missing constant 12volt to pin 58.
Do you get a 12v at pin 58 when you plug in the oem ecu?.....because I cant see the oem ecu working without a constant 12v there anyway.
And dont worry about pin 3&5 on the relays as well, they could be either way around once one goes to pin 49,59and 109, and the other goes to a 12v once the relay is energized.
Likewise with pin 1&2, once one goes to pin 16 and the other to a 12v
Have you tried placing the missing10A fuse as per Pauls faq?
Otherwise, you are good to go with with hard wiring it as you suggested.