> Is there a way to detect this and back off as soon as it happens, before the other system's owner gets annoyed?
You send a RARP, reverse ARP request, asking for who has this ARP to reply with its own IP, if no response nobody has such a MAC.
You can also change your MAC by sending an unsolicited gratuitous ARP with your IP address and your new MAC, without breaking TCP or UDP connections.
Unfortunately these systems fails if one of the PC on the subnet is not listening, in a deep sleep mode or temporarily disconnected from the wire (a HUB maintains LINK-UP to the PC but the upstream HUB link goes down).
Then, next time the PC wakes up and try to continue using the old MAC address to continue a TCP connection, it will talk to an unrelated PC and receive a RST packet, without checking that this MAC address is still valid for the TCP IP address.