I know the way many model builders get air bubbles out of silicone or other clear glues is to put the object in a vacuum chamber. But, I don't know where you'd find a vacuum chamber big enough for a CRT.

Plus, many of those glues like silicone and shoe goo are air curing and I don't think the stuff would ever really cure in the center of the CRT face. Besides, they may dry clear, but I'm not sure they'd be considered optically clear.

There are optically clear glues and UV cure glues that might work in this situation, but I'd bet it would costs a bundle for something as big as a CRT face.