There is another possible option:
Put in a switching proxy on all interfaces that diverts to either the old or new system based on account number.
Move accounts over in small batches.
OK - there remains the problem of account operations moving money between accounts on the old and new systems but that can at least be done with some batch mode glue rather than needing to be real time.
Disclaimer - I have never worked with a banking system but I'm applying general principals to the problem. Certainly in my line of IT work we always try to have the old and new system running concurrently and move the load over in a graceful way.
It would take some work to put proxies in place, but rather than being a short term hack, these can be very useful for load balancing and could become a permanent part of the design.