We have a Big Country 3950FB which is the same exact floorplan. We replaced our front bath toilet with a Dometic 320. From center of mounting point to back of toilet, you gain about 1 1/2 inches. It will work, but with issues. Note that in the BC and BH, the toilet sits on the door side of the rig at an approximate 45 degree angle. The Dometic, due to the added depth at the back, will sit in there but at less of an angle. Ours is wedged in at about a 30 degree angle, which puts my right knee into the cabinet when I sit on it. Additionally, the back corner of the bowl deflects the wall in behind it about 3/4 of an inch. If I rotate it more, the back corner of the toilet would eventually split the wallboard.
Short summary - it will fit but not without either modifying the wall behind it or compromising on the angle that it sits in the corner. I didn't even debate on trying to move the drain forward in the floor. Just not something I'm willing to undertake and, as mentioned by Tom regarding the LM, would probably be constrained by the frame. The toilet drain (and most of the plumbing for the front bath) is located in a foot wide section between the pass-through storage and the front storage compartment. This is the same area where the frame comes up from under the pass-through storage and is probably why moving the toilet drain is mentioned as a limitation due to frame issues.
Edited to add a quickie graphic of how the frame lines up on these models. The blue is the pass-through storage, the red is where the toilet drain drops to the tank below. (Not to any exact scale, mind you).