Yes, you can easily make the reflector, but there is barely any room under the bulb in most of those lights, so mounting the reflector can be a problem. Just use thin sheet aluminum, around .03 inches thick. Roof flashing is fine. Cut a piece as long as the bulb. Use a couple of boards clamped on each side of the place you want the aluminum to bend. Use another equally long board and a hammer to bang the aluminum to bend it. Repeat on the other side. Then adjust the bend angles so you can see an image of the bulb on each side of the bulb when you look straight at the bulb. Exactly how you attach that reflector to the light strip depends on how it is made and what you have available. I think epoxy will hold it, unless you are trying to adhere it to a plastic part. Two sheet metal screws will, but you have to be careful not to hit a wire or the ballast when you drill for them.
The aluminum doesn't have to be finely polished, but should look shiny.