For the difference in $ to buy a different stove, you could completely redo the whol alcove and come out ahead. I would spend a bit of time following up on the ideas above, even if you knock back the side walls one tile space each it should work fine. If you put tile-on-cement-board false side walls with a 1" airspace behind them on either side you'd probably achieve clearance from protected surfaces (or whatever the code language is). Maybe a weekend project, but a worthwhile one if you can keep and use that great stove.