Towing Capacity

Being close to the limit is no problem if you aren't over on tires, axles, or hitch ratings. There no reason you can't go right up to the max rating. I assume you mean your GCWR is 13,500; that would be the total weight of the TV and the trailer.
If, even at the rating of your rear axle and tires, you find the back of the vehicle squatting a lot then helper springs can help bring it back up. They won't make the axle or tires stronger. If you're over the axle or tire ratings then you have a problem.
If you hook up and are over your GCWR I wouldn't sweat it too much if you aren't exceeding any other ratings. However, you likely will be.

It sounds like you're falling into the trap of looking at tow capacity and GCVWR when you should be looking at payload and your rear axle rating.

Don't know who told you that but they told you wrong. Helper springs will do nothing but help hold up the rear end. They do NOT increase any of your weight limits or help with the limits on your tires, axles, wheels, drivetrain etc. etc. etc.
All they may do is help keep your headlights from aiming at the squirrels in the trees at night but the weight distributing hitch should do that also.
Barney