Tony,
Not sure how it should work in a mix scenario.
But first, in your business role, you have both BPIDENT and BPIDENT_MULTIPLE functions maintained. Its either one or the other.
For testing purposes, did you try to maintain only BPIDENT with B2C, and test again your scenario. In my sandbox environment, in B2C scenario, I don't get any message when interacting from the inbox. When I switch to B2B or MIX, I get the messages. The systems tries to determine an account from the one order data. From the account, it tries to determine the contact. No account is determined => first message. Then, no contact found (for no account found) => second message.
Therefore, I am not sure you can get rid of these messaging with customizing only ...
Sylvain