Routered faces backed by acrylic have been around a long time and they can be very durable.
The industry standard for the face is .080", or even 1/8th", with studs welded to the backs for attaching the plastic. Holes in the plastic to accept the studs should be twice the diameter of the stud—holes smaller than this may not allow enough room for movement of the plastic. Fasteners can be "speed nuts." Just push them on and don't tighten.
ACM is unsuitable for a routered face. You can't stud-weld to it and you may have delamination of the paper-thin aluminum from some of the pieces, especially the pointy ones. Most of the ACM products we typically use are only rated for five years anyway. Plus, ACM is not really rigid enough. This type of sign is not inexpensive to build. Why cheap out on the face?
On the other hand, why use polycarbonate? 3/16" acrylic is plenty strong for this application. Plus, it's easier to work with and it stays white.
Using tape and silicone to hold the plastic backer, instead of studs, is inviting the plastic to separate from the face, in my opinion. And in the event of breakage, replacing a stud-mounted backer is easier than one glued on. I also like using smaller, multiple pieces for backer, rather then one large piece of acrylic that backs the entire face. Assembly is easier and the movement of the plastic from expansion, especially long ways, is less.
Brad in Kansas City