Trailer shopping advice needed.

I haven't been to a scale yet, but my gvwr Is 7650 and the cargo capacity listed is 1823 which Includes a full tank of gas. As stated, my truck is a 2013 ford f150 super crew xlt with the ecoboost and max trailer/max tow packages. The only thing added was a line x spray in bed liner, which I doubt added more than 20 lbs. Adding myself and the family would add about 450 lbs. I figure I have a thousand lbs to work with leaving plenty of room for gear. I should be maxed out with a 7000 lb trailer and 5000-6000 being a target weight. Please correct my math if I am way off base here and I know this is a crude estimate.