I think you could use some 1/4" or 3/16" plate as a gusset. You would have to bend it to match the curvature of what is already there but it would really stiffen it up and still not look like a stupid add-on. Go about 6" on the vertical piece and wrap around the edge of the horizontal bend. Don't do it as just a triangle, add some curvature to make it look like you planned it.
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