"Can I attach a letter written by the client requesting the IRS to deposit funds directly into any of their bank accounts?" 

Winning the Powerball has better odds than the IRS reading the note and complying with it.

How about waiting for the new address to submit the 1040-X?  Or if local to you, how about using your office address?  A parent's address, a friend's address? After they have their new address file the Change of Address Form 8822.