Transport service failure and accumulating TRN*.LOG files, filling disk

Windows SBS Server 2008

Exchange 2007

Suddenly my long-running Exchange box has started crashing the Transport service. The sequence goes something like this:

Start the Transport service (either manually, or through reboot) with clean Queue folder.
Mail flows fine, but as it does, the mail.que file begins to grow, and TRN*.LOG files accumulate.
Eventually the disk fills up, the Transport service can't write to disk any more, and it craps out.
If I clean space from the disk, then try to restart, The Transport service begins the sequence of replaying the TRN*.LOG files, but it never finishes and eventually the service stops (again).
If I rename the Queue folder to Queue.old and create a new, empty Queue folder, Transport service starts, but we go through the exact same sequence again.
NOTES

I've investigated this post and performed as many of these functions as seem relevant on an Exchange 2007 installation - https://social.technet.microsoft.com/Forums/en-US/c7e6b5f4-ae0b-4233-bf10-13b533a49aab/event-id-7031-followed-by-7032-the-microsoft-exchange-transport-service-terminated-unexpectedly?forum=exchangesvrgeneral
I turned ON circular logging (it was off on all my mailbox databases)
I've disabled Transport Agents
I've disabled antivirus (Defender)
I don't know what to do next. Ideas?