I got DH using non sulfate any other harsh chemicals free body wash for a while - made a real difference to the duration in which i had to clean my shower screens....but now, he's gone back to plain ole soap - which is the cause of this grime IMO.....

I use gumption and scourer....then wipe it down with vinegar and water and chammy.

Ive heard having a sqweedgy (sp ??) in the shower helps...and after every shower just wipe down the doors etc...but training Dh to do this will be a chore in itself.