What about a white glass with some color swirled through it? It wont look like light covers and could match your decor.

Yes, there is a solid plain white available. Sometimes in mosaics that's all you need to make something really pop. Not sure what look you're going for, but here's a link.

http://www.stainedglasstile.com/snow_white.htm

If you want solid color, why not just go with a laminate insert?

Why not paint the back of the glass, or buy some spray frost and spray it till you like it.

the imperfections thing is kind of hard to overcome sense most pressed and rolled glass is trying to appear close to handmade.
you may have to look at the wispy opaques.

but here are some textured choices

Here is a link that might be useful: white stained glass

Cheat --- use plain glass and frosted clear contact paper over it . No one will ever know !

( That's what I used on my light box to diffuse the light - works great ! )

There is quite a variety of textured glass, some is more transparent than others. I would suggest you visit a stained glass store or a glass business that does decorative glass.
I'm having a hard time imagining white glass inserts.