Funnily enough I have just done the same job on mine, although an Irish sea Steamer still acetate sheet onto painted white metal.
I cut the sheet to sit on the flat of the internal face of the frame because if I tried to fit it into the frame itself the sheet was always flexed slightly and caught the light wrong. So I held the acetate sheet in the right place inside and I touched the edge of the sheet with a paintbrush loaded with watered down white PVA glue. The glue dries clear and does not mark the sheet in any way. When this first application had dried I went over it again to ensure it was sealed around the edges completely.
I am sure if I stick my finger through it it will push out but then I think that would go for a lot of glues anyway and I have a nice flat glaze with no glue marks at all.
You can just make out the glaze in this picture.