Our customer wrote a check to "John Doe" and left it with a waitress at a local restaurant who was to deliver it to the payee. She gave the check to "John Doe" who brought it to the bank and cashed it with proper identification. Turns out she gave the check to a DIFFERENT "John Doe" than our customer intended.

Is there commentary available anywhere in the UCC that speaks to the negligence that caused this check to be paid to the wrong party?

There is.. UCC 3-404 "Imposters;Ficticious Payees.

The bank has no liability under section (c)
"an indorsement is made in the name of a payee if (i) it is made in a name substantially similar to that of the payee or (ii) the instrument, whether or not indorsed, is deposited in a depository bank to an account in a name substantially similar to that of the payee."

Your customer can take this issue up with the waitress, or consider in the future giving checks directly to the party they intend, but they cannot come after you for cashing the check.

I agree that a bank has a defense against a forged endorsement claim when the drawer (or the drawer's agent) delivers the check to the wrong person, but suggest you are going to need more than subsection (c) of 3-404. Paragraph (c) only applies to the circumstances outlined in (a) and (b).

Practicality would indicate that a bank has no way of knowing if this is the "correct" John Doe. If it turns out that it wasn't, but this one got the check through negligence in the delivery method chosen, the loss falls on the drawer. Time to call your lawyer.