I live on hilly ground, too. With my 60" bucket on the DX29, I think the big thing the QA adds is not so much weight as additional length to the lift arms. Yeah, it's only a couple of inches, but that bucket is a long ways out in front of the front tires.
I have a block of concrete on the rear hitch of my tractor. I didn't build it, it came with the property. It measures about 3 feet high, about 2 feet front to back, and about 20 inches wide. There is a hole through it which I forced a 5/8 steel rod through, and a steel plate on top to which I welded a couple of pieces of large angle iron after drilling them. I figure the thing weighs about 900 lb and it does a lot to stablilize things. You could probably make one up pretty cheaply with some simple but well reinforced plywood forms. Put the hole in for the cross member by using a section of PVC big enough to pass a 3/4 or 7/8 steel rod through (I bend my smaller one from time to time), and use that for the lift arms to connect. You can set whatever you can come up with in the top for your top links. If I remember right, concrete is about 168 lb per cubic foot. You can save some cash and add more weight in less space if you fill the box with large field stones and work the concrete around them. They're more dense than the concrete.
In addition to the rear weight, I have 130 lb. of junkyard steel pieces that I welded up for each wheel. The weight on the sides does a lot more than the weight centered in the back for roll prevention, but the big weight in the rear makes the FEL work feel a lot more stable.
Before you get too carried away with the idea of digging up trees with the FEL, you should try just digging a couple of deep holes with the thing. A bucket is not a highly efficient digging tool unless you want a much bigger hole than you need. It may work with your sandy soil, but I really think you might want to check with a dealer about what is the best way to get those trees out without buying a backhoe.
Are you planning to save them, or just remove them? You could just cut them off and have the stumps ground down a foot or so.