I managed to speak to EI just before we got the airport.
I was told that it was BA that reprocted us.
Anyway, the kind lady over the phone rebooked us on this morning's EI flight to ORD. So it's worked out pretty well for us.
We're now sitting in the 51st&Green lounge, which is gorgeous! Preclearance is awesome by the way!
Now I need to cancel our tickets from BOS to ORD. I think one was a refundable fare, but the other one certainly isn't. Hopefully Amex Platinun insurance will refund.