Page 30 of the towing guide lets you know what axle is on what truck. So if the code is 26 it is not limited slip and is 3.73:1 rear ratio, while L6 is the limited slip 3.73:1 rear axle. Both of those come with the Max tow package, required for the higher GVWR.
So maximum 7,850 GVWR only comes with the XLT and higher packages. 7,600 GVWR comes with specially ordered XL trucks, with the Max tow and max GVWR 627 package in the build sheet.
The towing package is 53 C if it includes the trailer braking system, and will include the transmission cooler, 7 pin wiring harness, upgraded bumper, upgraded stabilizer bar.
Tow package 53A does not include the brake controller, or bumper or rear axle upgrade, but will include the 7 pin wiring, and stabilizer bar. This is found on page 14 of the towing guide.
So if you want a simple way to find the maximum GVWR, ask if they have any F-150's with the brake controller, thus they have towing package 53C, and the upgraded axle, bumper, ect. And should have the 7,850 GVWR!
Good luck!
Fred.