The red '
A' you pictured was a single letter, but you're indicating you're gonna make a solid box cut out with vinyl or digitally printed faces.... kinda like a free-form channel letter.
If you're Hell-bent on doing this yourself, why don't you just laminate with an outdoor glue a mirrored finish to a 2" piece of HDU ?? Mask the mirrored side while being CNC routered. Leave the mask on and spray the edges. Insert a few set pins in the back and glue fast to the wall from a pounce pattern you made for the guy CNC'ing the letters. Or just order what you need from Gemini. They have exactly what you need. To get some extra relief off the wall, just do an off-set stud combination.
We do this all year long inside and outside.
You talk about learning to become a signguy. First lesson is to not always say yes, if you can't even do step number one of the entire project. Sure, you hafta learn, but not something like this at a customer's expense. There's no way you can do this without subbing the vast majority of this out. Let's go a little further..... what do the permits cost to instal this thing or aren't you installing it ?? Also, as a sign business, are you qualified to go up there and do this kind of work ?? Does your insurance cover you if you fall off a ladder or drop a tool on someone's car or head ?? What happens if the glue starts oozing out from the heat onto something expensive below you and you don't see it right away. Are you covered ??
You need to explicitly ask your insurance company what you are and aren't insured for, cause after the fact, you can't afford for them to say, sure you have insurance, but not for something like that........