I kind of have your problem but in an apartment. Obscure glass is mandated by municipal law BUT when the light shines just right you could be a silhouette in the shower. Noticed that traveling on a city bus one day and decided that I needed to "fix" the problem even though I live on a higher floor. My personal solutions dinna have a screen door to monkey around with yet if it did I'd look towards a ceiling mount window shade. Just be sure that the shade's box (if it has one) will clear the doors' upper threshold. Off the top of my head I think a roller or modified balloon fabric shade would give you ease of use, clean-ability and clearance.