I looked into a flatbed for my SRW and found that I might gain storage but still did not have the payload to carry more. I was typically at 7000 lbs on the rear axle with the TC and closer to 8000 lbs when the fully loaded trailer was also connected. Although my rear axle had a 9750 lb rating, tires had a 9610 lb rating and the rims were rated 9000 lbs, I did not want to go heavier. When I tow the trailer, I have no need for additional vehicle storage - It is only when I was carrying the TC without the trailer in tow that I have wished for more storage.
You can lose a few pounds off the truck by replacing the steel bed with an aluminum tray (continue to use frame tie downs), but the steel trays typically weigh the same or more than the bed.