Well, it wasn't broken [1].
So of course, I fixed it [2].
This time, I managed to phase out the “old” router for the new “router” (even though they were nearly identical) without a hitch.
Woot.
Not so woot.
I forgot to update the routing information for one customer (technical explaination: I forgot to add their interface to the OSPF (Open Shortest Path First) cloud).
At least it was an easy problem to fix.