As this drawing sits right now, it's a neon nightmare. Theses are the types of signs that end up selling tons of LED's because this sign will be arcing and burning from many places. Sometimes, when letters can't be made wider and deeper, LED's are just a better fit.
I think as the sign company you HAVE to tell this customer that it would not be in his or your companies best intersest to use neon in this application. And if he wont budge, tell him to find someone else. I would not be involved in this project as it sits right now.
If he insists on neon then you have to insist on enlarging the letters.
This is like telling GM you want them to build you a new car, but you do not want brakes! (sorry, I use a lot of auto annalogies).
Sometimes you can not allow the customer to tell you how to make a sign.