We also have an '09 F250 (SD). Excellent TV and love it. I can't possibly see the need for extra springs. It does sound like you're overloaded. What is being towed, what's in the truck and what are it's specs?
Our tongue weight is nearly 1K lbs and we put a lot of stuff in the 8' box when camping which has a 200 lb canopy sitting on top plus all the weight in the cab (DW, dog, tools, bottled water and more). No issue ever with rear end sag.
A trip to a scale would be worthwhile. I found our actual payload capacity to be quite a bit less than what is shown on the sticker.
Spring bars need to be properly adjusted to transfer weight back onto steer axle. I have our bars adjusted to close to 100% restoration of weight removed with TT hooked up. The ball on the WDH should be initially set at 1" higher than the TT coupler with TT level. It's normal for the rear end of a TV to sag somewhat. It's the front that matters.
I believe the more recent F250s have one less leaf spring. Ours has 4.