I finally managed to get to the bottom of this one.

The problem seems to have been that the sending machine's clock (which is
also where the broker is) was 13 minutes behind the receiving machine's
clock and messages were being sent with a TTL of 10 minutes.  This seemingly
caused them to just sit in pending, until they then expired.

Increasing the TTL to 20 minutes solved the issue, as did manually adjusting
the time on the servers so that they were the same.

Both servers were set up to synchronise their clocks to an ntp server, but
it seems the relevant ports may be blocked on our network.

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