I hate reflections.
The only affordable way I know to place a piece in a location that has reflection issues like that is to use a media like one of the impressively lovely Epson Cold or Hot Press papers, and present it with absolutely no applied coating or overlaminate of any kind whatsoever. Just a bare print. That stuff (and most matte media) has wonderful resistance to reflections. However, the second you apply ANY kind of coating, you will have either bright specular reflections with a glossy coating, or more diffuse but much larger areas of hazing with matte coatings.
There is a myth that you can suppress reflections or hazing by using matte coatings. That is completely wrong. Matte coatings simply change small bright reflections to much bigger more diffuse reflections that are much worse than with no coatings at all. The only way reflections can ever be suppressed with coated or glossy media is to place the piece in a location that does not engender reflections.
So since your image is sort of out of harm's way from busy fingers, sneeze particles, and maybe even Windex raindrops, you may get away with a bare, matte print. If not, spend $500 on 1/2 sheet of Optium.
OK, there is one other possibility. Use an extremely bumpy media surface, and coat it generously with lots of gloss coating. What you will get is a presentation where you view a starlight sea of extremely bright highlights that nevertheless do not cover so much of the whole image that you can not make out that there's an image there. The effect maintains the sense of contrast on the surface of the print. In that situation you can still make out significant areas of the image around the tiny highlights. It's better than a kick in the pants, slightly.