I tow with a 2011 ram 1500 and am very close if not slightly over my max payload. I've done a lot of research.
One of the reasons for the low payload on the ram 1500 is due to the factory p rated tires. The rear axle is made by AAM and is rated quite a bit higher by AAM then ram. I've also heard that the ford payload package is simply different tires...
Another reason for lower payload is the rear coil overs. I have replaced the factory springs with super springs.
While neither of these improvements technically raise your payload rating, they can't hurt.
Of course a bigger truck is a better solution, but my Ram has been fine with 1500lbs of payload for the last two years. No mechanical issues and no towing issues. It actually tows better with more in the bed.