Making cabinets non-reflective without using non-reflective materials - help?

I have an interesting task, how does one limit the reflections on glass and perspex displays when using a non-reflective material isn't an option?

Thus far I have:
Diffuse light sources.
Angle light sources (both internally and externally)
Use info screens or hanging banners to block/diffuse ceiling lights/other conflicting sources.
Possibly try applying a non-reflective film...

Any suggestions?