I wanted to provide an update and acknowledge the product that Gunner recommended above. I just received 2 new direct replacements from SuperBrightLEDs for the 1157 bulbs. One was rated at 3W and the other at 4W (and more expensive). The LEDs I tried are the following:
The bulb in the foreground is the 4w. Both of these style LEDs did in fact fit in and clear the Backdraft housing. We have to go by our on own visual verification but the 3W style that is cheaper actually appeared brighter in the Backdraft Lens than the 4W style (in daylight and in dark) on both the stop and headlights on function.
Honestly we were impressed with the intensity of these LEDs over the standard bulbs. An easy swap and did enhance the overall brightness considerably. They do however seem to focus the light in a more narrow way since you are using 1 big LED or 3 big LEDs. Still think the clusters do a better job overall of increasing the overall brightness and doing it over a greater area that is less focused.
When I can get all 3 in a photo together for a comparison I will.
Sorry Gunner for discounting your suggestion without fully verifying. I had a couple older products from SBLEDs on the shelf that do not fit the Backdraft bulb housing.