I'm not saying you can't & I think after you load everything up you'll be maxed out (or close to it), but I think you'll be alright. Lots folks on here tow that heavy with a SRW. I used to tow our NP (same layout you're looking at) with a 2500. It just wasn't a "comfortable" drive for me, so I upgraded to the 3500 DRW. I'm sure you'll ge lots of opinions, but do what makes you comfortable.
'16 Ram 3500 MC CTD Dually, 4:10 rear
'14 Ram 2500 MC CTD (gone)
'14 287BHBE (gone)
'16 North Point 377RLBH (current and hopefully last)