Congrats on the truck! And this looks like a nice trailer!
I think people voiced the two sides to the coin already. You'll probably be over by a little bit, but don't sweat it too much. On a 7000 lbs GVR truck, 5% are 350 lbs. I'm sure it will do 5% over. Kind of depends on your style, do you like to follow all the rules or are you going the wink wink nudge nudge router every once in a while :)
Power wise you'll be super fine. I tow a similar setup with a 1999 F150 235 HP Triton V8.
Just make sure you operate with an honest weight calculation. Check the white/yellow sticker on the *actual* trailer because they can be significantly heavier than the spec. The thing also holds up to 800 lbs in the tanks.