Dizzy, the bands of light on either side of the centreline would be shifted further away from the tube with a double parabolic shape. I think I understand what you mean about the angle stock, but I don't think that will solve the problem of hot air collecting just above the tube.

The commercially made batwing unit I linked to has two means to adjust focus and beam spread. The reflector is somewhat springy and there's 2 stainless steel wires running the length of either end of the reffie, holding the sheet metal in the batwing shape. These wires have bits of metal clamped on their ends (like a bicycle brake cable). There are several holes in the reflector allowing the length of each stainless wire to be shortened or lengthened, opening or closing the spread of the reflector, which changes the spread of focus. The mounting for the tube socket also slides up and down to change the distance of the tube to the reflector. Sliding it all the way up toward the reflector spreads the beam wider, dropping it down narrows the spread. Mind you, once these two adjustments are set, they really need never be changed. The commercial unit makes this easy, but there's no reason why you can't cook up your own adjustment methods.

A crease and a little rebending action would very neatly make your new reffie act just like the commercial units. You could also cut the reflector in half and pop-rivet your piece of angle stock down the centreline, creating a neat 90 bend just above the lamp tube.

I do have to mention my misgivings about a highly polished surface on the reflector. If the reffie is highly polished and of single parabolic shape, one stands a very good chance of having focussed hotspots. Commercially made reflectors usually have a dimpled or textured surface or are painted/powder coated in flat white to more evenly spread light and avoid focus points.