I used the specs on a 2011 Dodge Ram 1500 2WD, with a 5.7 Hemi for this evaluation; so the specs are probably at least as high as your 2003 model.
The Ram 1500 models just do not have enough load capacity to tow 7000 lbs; regardless of cab style or bed length. The Ram 1500 has a curb weight of approximately 5,000 pounds. This truck is rated at a towing capacity of between 9050 and 10,200 pounds; depending on bed length. The towing capacity includes the GVW of the truck and trailer. So there is about 5,000 pounds beyond the truck's curb weight available to tow in the Ram 1500. You said you would probably not exceed 7,000 pounds GVW in the trailer. 5000 plus 7000 pounds is 12000 pounds. This would be one ton over the truck's maximum rated towing capacity.
A 5.7 hemi powered Ram 2500 has a towing capacity of about 15,000-15,500 pounds; along with a curb weight of 5600-6100 pounds. So it could tow a 7000 pound trailer with room to spare.
I'm sorry that it turned out this way; but I believe it would be dangerous to tow this trailer with a truck that is loaded a ton over its rated weight limit.
In view of the extremely high gearing; I would not use overdrive when pulling a load this heavy, even on flat ground. 2500 RPM is the lowest engine speed I'd want to see at freeway speeds.