The worst for that was my Triumph Trident that had a rear drum brake as it started to heat up so it would gradually start to work. Back wheel braking was always a must in icy and snowy weather or rain after a long dry period and the roads are very greasy and slippery as you can fishtail all day long, but once you've lost the front......

On the Kawasaki the original pad were useless in the wet, dangerously so, as you had nothing for a wheel revolution or two until the pads had cleared the water off the disc, then they would start to bite, but the danger was always to make sure you didn't over brake as the natural tendency was to pull on the lever more. This I cured by using dunlop sintered pads, which were great but at the cost of speeding up the disc wear. I replaced these with EBC disc, braided brake lines and their kevlar pads, but in the wet the hesitation was back. Bike has been off the road for sometime now due to the effects of the recession, but going back to sintered pads will be a must when I put it back on the road, plus I need to get a master cylinder service kit where the front brake lever now pulls all the way back to the handle bars!

Back brakes on bike have very little effect on braking, where the majority of work is done by the front. GP riders used to use the back brake as a form of manual traction control before that was fitted.
Going back to Omega brakes, then bigger discs will help with heat dissipation, but will it be enough, I suspect not. Four pot and six pot as you say will increase the pad area, but will also increase the heat generated. A possible solution would be harder pads that work to a higher temperature, but your then making another Omega brake problem worse with relatively long pedal travel and lack of initial bite that Omegas suffer from as the pad will need more heat to reach full efficiency, although braided hoses would help in firming up the pedal. I don't know how good Omega calipers are with regard to expanding on braking as they always look a little weak to me.
The other issue is cost as I would imagine 4 pot aren't cheap and 6 pot are only going to be more expensive.
With any ducting could you get away with a front spoiler hole and a hose to the plastic inner wheel arch as there has not only got the be clearance for the suspension but also for the steering. Lozzz's picture of the Omega with the engine remove looks as if that would be a possibility.
Lot of questions with few answers I'm afraid.