For those who want to try to keep the glass cleaner,, see if you can find a fine mesh screen, like a screen-door screen.. and place a 'curtain' of the screen between the fire and the glass.. I think about 1/2" to 1" from the door would work best..
A lot of the haze is created by the hot pieces of ash flying off the fire, hitting and pitting the glass.. with a screen between the fire and the glass a lot of the pieces will hit the screen and be deflected,, not all, so this is not a perfect answer..
There was a stove with this screen as an option,, I don't remember who's stove it was.. maybe coal berner will chime in and use his encylopedia memory !
A piece of SS screen would be best, but I'd experiment with inexpensive metal door screen first to test the effectiveness of the idea.