I have the same 10k hitch and the max. tongue weight is 1k.
So I struggle with the same issue.... It's real close, but technically over!
My measured trailer tongue weight is about 1,150 lbs, so say 1,200 lbs. as well.
However, this is the hitch that was sold to the original owner of my trailer by the dealer.
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2012 Lacrosse, 308RES.
2013 Ford F150, XLT, 4x4, Supercrew, Eco-Boost.
Lee, Dawn and "CoCo", the dog!
2015 Overnight Camping Days = 25, States Below: