How much of the inside of the box will be visible? You could mount the box to the top of a hard hat, or if it’s really light you could use foam to secure it to a baseball cap with the brim removed.
Whatever you do, make sure it has adequate ventilation. Nothing will make you feel uncomfortably hot like having no airflow across your head/neck area.
All of the interior will be visible - the purpose is to make a 2 dimensional frame for my face, so don't even need the rest of the box if I can figure out how to suspend the frame
My first thought would be to get some plexi and make a shoulder harness with a small weight on the back to counter the weight of the frame so it doesn’t slip too far downward.