LEDs

That's probably +/- 10° on axis. Most high brightness ones are around this value. You can get wide angle (110° versions?) but probably not locally and not in small quantities. It might be worthwhile checking the Farnell and RS catalogues (both are online).
Best solution is to use a diffuser, like a piece of the knobbly plastic used in ceiling panels in front of fluoro tubes, if your break lights are not made like this already.
Alternatively you may have to mount some of the LEDs at an angle.

I had a look there and also at digikey.com and couldn't find anything that suited. There were some with a 40 degree viewing angle which is a little better.
I've had some success sanding the surface of the LEDs, in fact it has been a huge improvement but it's a bit patchy in it's appearance. Maybe I could dip them in a solvent that would disolve the surface slightly?
Michael

a dip I would suggest heat, perhaps a good (say 80w) soldering iron? Chopping the top off in a prismatic fashion should get good results in dispersion.
Course, you still want some pointing directly behind you to warn the bloke who's right there, perhaps a combination of filament bulb for side view and LED for instant warning?
-mark

And why not just put another damn bulb in. It's been designed to meet many safety standards and is cheaper than a LED.
I don't see what you'll achieve other than an insurance cancellation and the loss of useful drinking time.
-Andrew M