OLED behind acrylic glass

Hi, not that much an electronic question, but perhaps somebody has an idea: I want to build a case with an OLED display module. The idea is to have a sheet of acrylic glas, behind which the OLED is. The rest of the sheet is to be spray painted black. Optimally, this should look like a glossy black surface with an almost invisible display when it is off.

A first test, where I just pressed the display against the acrylic glas sheet with a bar clamp failed. I hoped that it was tight enough not to let dye in, but apparently, capillary forces did their job. The Display is indeed almost invisible when it is off, but it has black spots.

Next idea would be to first glue it to the acrylic glas. To get the glue even, I thought about using spray glue and spray it on the display. Can anybody recommend a glue (spray or with a plan to get it on there thin AND even) that could work to combine real and acrylic glass?
Most brand spray glues here cost 15€ per bottle and I would like to avoid having to try multiple ones.

A thin layer of UV-cure resin?

might be a good idea. But how do I get it thin? I would like to avoid bulges on the sides since those may be more visible after the spray painting. On the other hand, I cannot have uncovered surface ...