If I'm not mistaken, the tow ratings are pretty close to the same for 350 SRW and DRW.

Are you just looking at the different tow ratings based on gears? You can change the ring and pinion in your current axle from 3.73 to the deeper gears and the truck will have those capabilities.

But as others mention, changing the truck's capabilities does not change its "legal" tow ratings. Many folks do violate the legal ratings on a regular basis, but I encourage you to know the possible risk to do so in your neck of the woods. Every state is different.