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Check the source: does UDP mode have Don't Fragmet set on
the outgoing packet? If so, that could be the source of our
intermittent Message Too Large error.

1191 outlines a few strategies on figuring out the proper
MTU value to use, but I think the simplest one for our
stateless setup is to reduce by a certain number each time
and signal the remote end that we're doing so, maybe even
with a proper 1191-format packet.