Finally a pic of the wiring:
The new fan wiring is all sleeved and runs alongside the original fan wiring. I've disconnected the 1st speed wire from the resistor pack and bolted it and the positive of the new fan through the heatsink / backing plate using nylon insulators (circled in red). The negative for the new fan is bolted straight to the heatsink as that is grounded to the body.
So, instead of the original fan coming on at its 1st speed, the new fan comes on at full speed instead. 2nd and 3rd speeds on the original, if they're ever needed, will work through the resistor pack as normal.