From the scale weights the OP gave I get a trailer weight of 10360 lbs and a pin weight of 2160. Lbs.
That gives a pin weight percentage of 21% which is on the low side of desired.
5 th wheels do best with 20-25% pin weights.
Typically better in the 25 % range.
There are thousands of 3/4 ton trucks pulling 10,000+ lb 5th wheel trailers with no problems.
I agree the hitch needs to be moved forward such the front axle weight does not decrease with the trailer. Adding weight to the front axle is ok and will help with weight distribution and improve towing.