Probably a version of the F250 trans like you mentioned... I don't see a dual clutch handling the power and/or off road abuse. @FordTechOne probably knows what would fit the bill better than me.
Super Duty uses the new 10R140. It’s a massive transmission in both size and weight; it would not be suited to a light duty application like the Raptor, even with a supercharged V8.
Raptor R will almost certainly be a 10R80 with the necessary enhancements to handle the extra power and torque. The Tremec TR-9007 DCT is a high performance car transmission, it’s not designed for towing/hauling. From what I can find the maximum GVWR is 5,291, which is less than the dry weight of a Raptor.