There is only 26 inches of wall before a window in one corner and about 33 inches in the other corner before a window. Of course, we would prefer to put it in the smaller corner for several reasons. In the preferred corner, the window is a small high one that has about 49 inches of wall below it so the fireplace could extend slightly below that window with a flat top mantle instead of one that goes to the ceiling.

I haven't been able to find anything smaller than a 33 inch heatilator but it still extends pretty far into the room.

Can anyone suggest anything that is designed to fit tightly into a corner?

If, after you do your search, you do not find any fireplace that will work, consider an alternative like a cast iron stove of a soapstone stove. They are a different look, but they are very energy efficient. You might find one that makes the kind of "fashion statement" that appeals to you. Google gas stove or cast iron stove or soapstone stove. Widen your horizons. I'm sure you'll find something that will work.

Good luck.