I have a 4110 with the 4110 FEL. I've used the FEL many, many times with wet dirt and mud and river rock. I usually have a 5 foot Frontier box blade on the back and I've never had a problem with the rear end getting light. I believe the box blade weighs in the neighborhood of 600 lbs.
I also have a ballst box that I plan on filling with sand, but I haven't done it yet. I believe that the ballast box filled with sand will weight around 900-1000 lbs.
I can't imagine having to fill my rear tires anytime soon. If I do finally get the rear end to bounce a little, I'll just put the ballast box on.
To be totally up front, I'm always very careful about driving carefully with a full FEL load, and I always drive with the bucket very low to the ground. My property has some pretty good hills on it and I do notice a little rear-end bounce when I go downhill with a bucket full, but nothing too serious.
I think driving carefully and watching the vertical position of your bucket and rear ballast are important.