Step 4: metal base
Most OE badges are made of clear plastic (either acrylic or polycarbonate), with embossed patterns on the back side to facilitate for the chrome lettering and painted base color. The molded plastic piece also has built-in recess so that automotive grade double-sided tape can be placed on the back but no adhesive edge shows on the sides of the badge.
With a DIY, I wasn't sure if placing the dichroic coating plus base spray paint would make it durable enough not to peel off over time.
My solution is to let a piece of sheet metal hold onto the double-sided tape by adhesion, and then have it also hold onto the acrylic piece by mechanical means (i.e. having the metal "clamp" onto the acrylic piece). Then, all decorations will be done on the inner surface of the acrylic.
There's a type of aluminum sheet metal that is readily available in most hardware stores in north america; it is sold for roof flashing by the roll. Household scissors can easily trim it with reasonable accuracy. While aluminum is relatively more brittle than steel, this particular product isn't too bad unless you make too many erroneous bends... after which it will fail at the bend. A piece is cut, shown next to the acrylic piece.
Using a pair of pliers, gradually bend each side to increasing angle up to 90 degrees. This will serve as the metal frame that will keep the acrylic piece in place.
In this step, the cardstock template also plays an important role. The folded edge of the sheet aluminum should conform to the template opening: