Slow remote SELECT statement due to long "client processing time", but fast locally
This issue is now resolved.

It was a network problem, and the SQL box was using a 100 MB/s NIC card, instead of a 10 GB/s NIC card...

A network configuration change to use the correct network card has fixed the problem.  Now we are getting similar performance for all queries from the Production SQL box and from other boxes on the network.

Thanks everyone for your help.