I worried when getting my new 5th wheel a couple months ago. My truck is a 2014 2500 w/6.4 Hemi 3.73 gears. My 5th wheel is a Keystone Hideout and was surprised to end up with about 8" of clearance. I think some RV manufacturers are catching up with the height of these new trucks and building the 5th wheels accordingly. The worst combo would be an older 5th with a newer truck. So, you might check out some other brands of 5th wheel and you will probably be okay.
Now for the weight thing. Your max weight should be 12,500# with a payload of 3000#. I have a 12,000# GVWR 5th that, once loaded, puts me right at my payload max. The 5th overall weighs about 10,500# and leaves me about 1000# of GCWR (combined truck and trailer max is 19,500#).
GCWR:
Truck - 7000#
People, 5th hitch, etc. - 1000#
5th - 10,500#
Total = 18,500#
Payload:
Truck - 7000#
People, 5th hitch, etc. - 1000#
Pin weight from 5th - 2000#
Total = 10,000#
The truck handles it fine as is but I'm likely going to get some rear airbags as it bounces a bit excessively over uneven roads at times. Nothing terrible. I'm also thinking about re-gearing with 4.56s. The same truck with the 4.10s is rated for an additional 3000# of GCWR (payload stays at 3000#). Aside from towing better I've also heard good things about the truck as a daily driver with the different gears. The only downside is I'd be turning about 400RPM higher on the freeway. I can't remember exactly but I think it's like 2200RPM vs. 1800RPM at 70.
Edit: I see the OP is in Florida - I'm out west with lots of hills so. The 3.73s would be fine in flatter areas.
