Get a large sheet of metal, ideally the kind used to make heat-shields for cars or used to make flashing for fireplaces. Build a mobile screen in front of the stove. Paint the whole thing with black exhaust paint (used in cars...very safe here).

Voila'! Fireproof. Mobile. And no nasty reflections.

And don't worry about the heat. It will be bounced back towards the stove and disipate into the house. Or you could simply aim a fan at the whole thing...