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Couldn't say if there is a safe amount of clearance, but a hot fire would tell you. If its too hot a thin sheet metal baffles fastened to the inside walls and spaced away even an inch will reflect heat and allow air to circulate behind through convection. The wood wall will be considerably cooler. The baffles can be fastened with screws and spaced away from the wall with sections of small diameter metal tube.
If weight isn't a big consideration I'd put cement board behind and underneath the stove, doing that you're definitely safe even with five inches of clearance. All the home wood stoves instillation guides I've seen call for at least a foot of clearance on any side from a wall.
I actually ended up lining the bump out with cement board. I brewed up a couple good fires and the board got ripping hot but doesn’t burn. Works great.