The FPN does nothing more than remind you of an accepted guideline, or design goal.

So what is this voltage drop issue all about?
In the first case, it's about days past, where a 120v service might actually be delivering only 120 v to the customer. Lose a few more volts, and you no longer have the minimum 108 that a 120v appliance needs for proper operation. Of course, these days I quite often measure incoming voltages that are much closer to 130, than 120!

Secondly, a large voltage drop is a suggestion that there MIGHT be a problem. Far more than wire length, bad connections will cause such a drop.

It might be interesting to do the voltage drop test at the panel, as well as at the receptacle. Then, progress along the circuit, and see if the drop is gradual - or happens at one place.

If, even with the drop, you have more than 108 v at the receptacle ... and there is no mention of this testing in the contract ... I don't see a need for you to do any more. This time. What else you do is more of a business decision than anything else.

As mentioned earlier, a 'quick fix' would involve replacing the home runs with #10. Putting junction boxes in the attic, and replacing the bulk of the run, just might make everyone happy.

Otherwise, you've received a 'wake up call.' I'm sure you will forever consider voltage drop in your future work. Because, legalities aside, you can see where 'code minimum' and 'good design' are not the same thing.

As for the HI ... well, everyone has an opinion. Keep in mind that the HI is not the one licensed to do electric work - you are - so by definition you are qualified, and he is not. Keep in mind that he is not, in any way, the AHJ. He's just a spectator. You have no contractual relationship with him, and have no obligation to care in the slightest what he thinks.
If the customer is not happy, he can pay you ... and not hire you again. Or, future jobs will be planned / priced with this additional requirement in mind. Or, you can be NICE and accommodate him this time, for the sake of future business.

But the FPN has NO code significance, and is only a suggestion, without even the weight of the code saying 'may' or 'should.' It's NOT part of the code. This is explained in the very first pages of the code itself.