>> I've already had several direct replies saying to manually configure the
>> 172.16 subnet on router A.  Sure, that will work, but I'm looking for a
>> solution that doesn't require manual configuration of all the routers
>> involved.

Put another physical ethernet interface in router B and
move 172.16.16.0/24 to the new interface.

This will get you over the psychological hurdle you are facing.

-mark

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