Although a different RV, last year we ought a Big Country 3560 SS. At that time, we had a '15 F350 SRW sb, cc,4x4, PSD, as we just bought that truck in Dec of '14. The BC specs from factory were: dry wt/13420, pin/2888, max wt/16,000. Weighed unit on a CAT scale on way home from dealer netted: empty wt/14,000, pin wt/2860. I was aok w/ steer axle weights. Just under rear axle by 500 and pretty much at truck max capacity of 11,500 completely UNLOADED! I knew I was going to be close on weights w/ everything, BUT NOT this close!. Once fully loaded, I was over on rear truck axle by 300 and truck by 860 with NO ONE in cab. Oh, pin weight now came in at 3680, and total weight for the BC was 15,980 or maxed out. With the BC hooked up, rear truck axle was 7300 (max axle: 7000), max tire capacity: 7280. Again nobody in cab.
So to say the least, we towed all last summer ('17) w/o any problems and a long trip to Bar Harbor. However, I had in back of my mind this nagging/gut feeling about the overall weight of things. Come summer '18 planning and trip to FL in height of summer (Aug) and NOW the weight of things was really eating away at me and the gut feeling got worse. Was always told to trust your gut, so we ended up getting a '17 F350 CC,4x4,PSD, dually. Admit-tingly, since we bought it, I haven't weight things and cannot explain why, but just haven't. I will say, it was a very wise decision and felt very comfy towing the BC down/back at 70 mph and w/ wife driving at times.
While I haven't looked at today's towing numbers for SRW trucks, personally, I'd be very concerned and nervous to tow a RV over 15-15,500 with a SRW. I guess you could say, "Well how many half tons do you see towing overweight?", which is true, but based on my personal take, I just wouldn't. To each his own, but IMO to answer OP's question about rucks, I'd opt for a dually from one of the mfr's.