My trailer is very similar to yours. (see signature below)
You are going to be pushing your cargo capacity by 400-500lbs when loaded.
If I remember right, the cargo capacity is 1450 lbs.
Your actual hitch weight will be 1300 lbs+-. Add your hitch, cargo, family, and there you are.
I added air bags to take out some of the sag in the rear end.
I only run them with about 25 lbs when towing and that seems to do just fine.
Also if you haven't already, you will need to upgrade your tires to LT's.
The "P" rated tire is to squishy for heavy hauling.
The truck has PLENTY of power! No issues there.
The six speed tranny does a great job.
I recommend the Prodigy brake controller.
Mine works great.
The connection point is behind the kick panel by the parking brake pedal.
You should have a pig-tail laying in your glove box.
There are lots of clever places to mount it.
I mounted mine on the plastic shroud right above the gas pedal.
You might want to visit : Tundra Solutions Forum
and talk to some other folks who pull lightweight fivers with the Tundra.
I can't comment on the Sidewinder becasue I don't know much about them.
I am using a Superglide and love it.
Overall my truck performs very well.