Hi John,
What is the IMAP server name from which you collect your off-site mail?? If this is "stmarys-school.org" then this would cause the problem.
The reason: your local computers will not be able to determine the difference between the local domain and the remote domain so as soon as it finds one, it stops looking. As a general rule, it finds the local one first. As you say, by changing the local domain to stmarys-school.lan (or .local for example) then your local computers will be able to determine the difference between local and remote domain and therefore resolve correctly.
I presume you had the same setup working with the old server? Was that setup with .org or .lan??
If the IMAP server you are connecting to runs at the domain "stmarys-school.org" then this is the only fix / work-around.
If it doesn't run from that domain then we'll need some more information to solve it.
Let me know how you get on.
Kit Norriss