We pull our Big Horn 3070 with a 2006 Chevy 2500 LB Crew Cab SRW and YES we do have a pin weight problem. Had the rig weighed at the Goshen rally and found it to be 250 over the allowed 3000lb max.
Had to unload as much as possible from the coach. Started by getting rid of much "might need" stuff from the front compartment and the basement and then went upstairs and unloaded LOTS of clothes in the front closet (this REALLY created tension with DW).
We couldn't "shift" the weight as there is really no place to store in the rear of the coach. Will see what happens next time we get it weighed.
Keep in mind that we do have dual pane windows and 2nd A/C. Also have the Level Up installed but do not know if that adds much. I did install air bags on the truck, but that does not increase the load limit, just the ability to keep the truck level (not really needed, but makes me feel better)
By the way, the pin weight was 3250 lbs last time we weighed and our truck and hitch each have a 3000 limit. It really does not take much to add to the pin weight with this coach, but we love the layout and have no plans to change any time soon.
I believe that Heartland (Lippert) needs to look closely at the location of the axles on this coach and perhaps move them a little bit forward since there is not much weight in the rear like on the larger coaches.