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Go with the 1,200/12,000 Equal-i-zer...., and based on a recommended 13% to 15% loaded tongue weight range of the 25BHS's potential loaded weight the 1200/12000 won't be an over kill.
Worst loaded weight condition of the 2012 25BHS would be it's GVWR of 8,180lbs which equates to a 1,063lbs to 1,227lbs (13% to 15%) loaded tongue weight range.
The 775lb hitch (tongue) weight you sited is it's published "dry" (unloaded) weight.
Bob
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2016 GM 2500HD 6.0L/4.10
2018 Jay Flight 24RBS
2002 GM 2500HD 6.0L/4:10 (retired)
2005 Jayco Eagle 278FBS (retired)
1999 Jayco Eagle 246FB (retired)
Reese HP Dual Cam (Strait-Line)