John,
Set one string in a unison 'flat ' and the one in the next unison
'sharp'.  By alternating this up the scale the overall tension will not
change causing further distortion of the plate and board. Make it
dissonant to the degree that the customer wants to hear.

In the future, the answer is to simply perform a rough tuning which
will not require the further attention to make it acceptable to the
customer.  If there ever is a 'next time', unless they are on a
periodic schedule for pitch maintenance, how will they ever know when
it 'needs' tuning :-)  ?

Regards,
Jon Page,   piano technician
Harwich Port, Cape Cod, Mass.
http://www.stanwoodpiano.com/