Well I tow at 19,000 to 19,500# GCVW. 2001 Ram 2500 5.9 CTD. Yes over the TV GVWR, but well within axle and tire ratings, almost 700# on the rear and 600# on the front to spare.
You will likely be very close to the 9,900# GVWR of the SRW F350, Yes.. Will the F350 tow it, yes! Will you be close to or slightly over the F350's GVWR.
The choice to run over the TV GVWR is yours and yours alone. I will say I tow a 5er about the same weight with my 2500, with no issues. I don't have or need air bags or Timbrien's.
Yes, I feel very safe and comfortable driving these roads at 55 to 60 mph. This is my experience, your may vary, I work to keep the front end tight no sloppy steering.
To Golden's comment about a TT with a 1,500 TW, I would rather see a family in a slightly over GVWR with a 5er, than running a big TT, the 5er is naturally more stable to tow.
Take a good look at your VIN sticker and look at the GAWR's for front and rear, are you going to be well within those? What tires are you running? What is their MAX load rating? My 265/75-16E's are rated at 3,415# each, that is 13,660#, so even if you hit 10,000# you would have 3,660# of capacity to spare.
