Found it.  The server properties, Connections tab specifies a remote query timeout.  This value can be overridden on the linked server properties Server Options tab.

Don't ya just love it when...

Update:

When I said 'When I run the remote procedure manually from the Query Analyzer,' I was connected to the secondary.  When I tried remote execution while connected to the primary, I...

OK, here's some results:

The 'select * from master..systemprocesses' shows some blocked processes with wait times in the few-seconds range, which indicates (according to Douglas) many small transactions.  I am inclined...