DRW with that one unless you pack VERY light. It is technically possible to stay within your numbers but it would be really a PITA.
I'm not so on board with the "just go by GVWR" thing. It's a # on a tag. It doesn't mean you WILL load to it (or even stop once you get there for that matter). Mainly, I don't like the theory because CCCs (difference between dry weight and GVWR) vary vastly depending on frame size, axle size and other factors. I once had a 26' TT with a CCC of 4700# putting the GVWR at 11,000# for a 6300# dry trailer. Was I supposed to buy a truck to haul 11,000# just because of a sticker on the door?
Many of you act as though it's impossible to just weigh what you put into the RV. It's really not that difficult to determine what YOU travel with an plan accordingly.