Your revised letter is good!

Be sure you record the SERIAL Number of the camera -
so you can tell if they DO replace it.

Also wouldn't hurt to include a COPY (Not the original)
of the FIRST repair paperwork...
They "should" be able to tell from their records that your camera
has made a previous trip in for repair -
but giving them the copy of the paperwork will make *sure* they know!

Also - check to see if you're supposed to send in the removable
"media" (storage card) - SOME of the repair centers advise
Not to Send the media (they use their own for testing).

Good Luck!

/s/ Phred