Viola! I had the polarity on my 12v power input reversed. Swapped those and the relays are now working perfectly!
The question I posed earlier about being able to run two input power lines through the emergency stop button remains. Right now I am only running the 1F power through the emergency stop and not the router so I am back on the air, but I would like to be able to run both power lines through the emergency stop if at all possible.