Just an update on this, I ended up ordering the relay mentioned in my earlier post (Omron MY4ZN DC48). As it turns out, the terminals were the plug pin type, wider with a hole for wiring.
I ended up using my Dremel to grind them down a bit, not my best work by any stretch of the imagination.
I did some more research and I believe the correct replacement is the following part number. Mouser and Digikey don't stock them, but they can get them with the lead time in mind:
Omron MY4Z-02-DC48
The connector type is listed as a "PC" connector, so it should be the correct pin form factor from the data sheets I looked into.