Check the GCWR. Most of the RV makers anymore do NOT downrate the factory GCWR of 22,000 pounds (Ford chassis). This means you can pull 7500 pounds even with a loaded RV. Winebago has a tongue weight limit, but others don't.
But.... you will need to replace the hitch receiver. E350 van receiver will fit, but an extra set of holes will be needed, and the shim-order will be different than on the vans (the shims accommodate the bumper brackets).
Also, double check the frame extensions were done to Ford spec. Ford says all ratings remain intact if the specs are followed:
https://www.fleet.ford.com/truckbbas/non-html/Q18.pdfFinally, you will need to make sure the trailer's tongue weight does not overload the rear axle. With most RV wheelbases, the tongue weight on the ball will result in 2x that weight being added to the rear axle. Look for the longest wheelbase possible for a given length coach. This may be affected by floorplan. Some 31' Cs have a 223" wheelbase but some only have a 208" wheelbase.
2000 Ford E450 V10 VAN! 450,000+ miles
2014 ORV really big trailer
2015 Ford Focus ST