I also experienced something similar, but my issue was that it didn't slide into place as easily. The upside of my issue is that it didn't slide out of place easily (like yours).
I think you are right to assume that more foam would help. Just be sure that you don't put too much pressure on the PCB or LCD. You don't want any real pressure. You just don't want it to move by itself.
Also, I'm going to edit the title of your post to include "Boxy Pixel Metal Shell" in it, to see if anyone else building those shells comes here to discuss the issue.
I also wonder if you could use some tape around the frame of the LCD to hold it in place.
I think you are right to assume that more foam would help. Just be sure that you don't put too much pressure on the PCB or LCD. You don't want any real pressure. You just don't want it to move by itself.
Also, I'm going to edit the title of your post to include "Boxy Pixel Metal Shell" in it, to see if anyone else building those shells comes here to discuss the issue.
I also wonder if you could use some tape around the frame of the LCD to hold it in place.
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Neo Geo Pocket Flash Cart and Linker Project ( http://www.flashmasta.com/ )
Avatar art thanks to Trev-Mun ( http://trevmun.deviantart.com/ )