I have done some of my own pickguard material laminating, with a home-made laminating press, which is, at the most fundamental level, two pieces of plywood that sandwich the plastic sheets, pressed together by a large number of clamps. There are refinements beyond that (for the purposes of alignment and containing glue squeezout), but that's basically what it is.
I did some with two-part epoxy, some with E6000, and some with strong spray adhesive (3M brand #90). They all work pretty well in terms of getting the job done.
Spray adhesive is the easiest to apply. Very noxious fumes, though. Make sure you use it outside, and with a good mask on. And there is absolutely no second chance with it. You align the sheets right the first time, without bubbles, or oh well; they're stuck that way. And of the three glues I've tried, it gives the the thickest glue layer between the layers of plastic.
Epoxy is easily the strongest bond, but you need a lot of it, and it's hard to work, being thick. It's also the hardest to press, due to that thickness. That is, the hardest to squeeze out. Incomplete squeeze out means inconsistent flatness. Definitely get the slow setting kind, and definitely thin it with a solvent.
E6000 is a good compromise between the two. It's a single part glue, in a large enough tube that only one should be enough. It applies and squeezes out more easily than epoxy. It's more workable than spray adhesive. And the bond is strong enough. All things considered, it's the best of the three IMO/IME.
I have also laminated cellulose nitrate sheets to make custom guards in the old style material similar to that used on '50s flying Vs and Explorers. For that, I used lacquer thinner loaded into an airbrush as the glue. You need to work fast, as it evaporates quickly. And this only works on materials that lacquer thinner will melt. I also suspect it would work with a paint brush, as opposed to a spray gun...but would be a lot messier.
There are plastic glues made for ABS, PVC, acrylic, and various other forms of plastic. They'd probably work similarly to the lacquer thinner method, but I have not actually tried them to laminate pickguard material. My lamination projects have always involved bonding non-standard or non-matching materials (Bakelite to polystyrene, for example, or the aforementioned cellulose nitrate to cellulose nitrate).
There is also a guy who does custom laminating, in Phoenix. The shop is called Precision Guitars. .060" of black with .030" of white on top of it probably wouldn't be hard for him to do. He has been sick, however, so he is far behind in his work.
Spitfire does custom laminating as well, but they are ungodly expensive.
FWIW (and while I generally don't like to endorse them), Stewart MacDonald sells a .104" W/B/W pickguard material on which one of the white layers is thinner than the other. If you put the thin layer down instead of up, it would probably disappear visually against a white guitar. This would especially be true if you were to, after beveling the guard, go around the perimeter with a scraper, eliminating the bevel on only the bottom white layer.