For comparison sake I have that exact 5th wheel (love it BTW) and I'm usually within 100# one way or another of my truck's 10,000# GVWR (3000# payload on 6.4 Hemi).
Sounds like I have very similar equipment and people - 250# slider hitch + wife + 3 small kids and an average amount of stuff in the truck and trailer.
As others have said you should be comfortably under your RAWR which is most important. I had some Firestone airbags installed and really like them. So, you might consider that if you haven't already.
To answer the heart of your question, as best I can tell my pin weight on that 5th went up about 250-300# from "dry" to "loaded". I never weighed it when new so I'm assuming the factory listing is accurate. And I've never used a pin weight scale or anything. The closest I've come is to weigh my truck on a DOT scale near a campground right before and after hooking/unhooking. And those only move in increments of 50# so it's not an exact science.