Here's an idea that may or may not help you. In my GTP I replaced the factory plastic fog lamps with some glass ones the same size. They take those little 50W halogen bulbs. I think having a metal relector that focuses may be more help than moving from plastic to glass for the lens. Anyway, oncoming traffic didn't like them so I made them high/low beam. Now some lamp housings may actually allow you to install a two filament bulb, which is another great idea. I didn't have that, so I used a relay to run the bulbs through a resistor on low beam and direct on high beam. The nice thing about filament bulbs is they get yellower as you dim them, in line with the fog/driving light idea. I think the resistor was about 0.8 Ohm, but the correct value depends on the bulbs you choose. Keep in mind this is a giant resistor - it should be rated for about the same power as the bulbs. Looking back, it would have been cooler to build a PWM controller, but I had some resistors laying around and it's been working fine for years.
There are DRL systems that run the bulbs in series. This is very simple and efficient, but I don't know if you would get enough brightness.
I think I have seen some housing that take two bulbs, which would be about the coolest way. So you could run a yellow bulb for "fog" and some killer bright bulb for "driving". 5.5" is a lot of room to work with.