Dave, I would generally agree with your advice to stick with the camera manufacturer's lens (should be a better match optically), but Fuji doesn't market a TC for the s6000fd (unless they have come out with one recently), and doesn't recommend use of one. Speculation in this forum and others on this site is that the company was concerned about the effects of weight on the manual zoom mechanism, most of the parts of which are plastic.
I have addressed the issue by purchase of a lens support bracket which I attach to either a tripod or monopod and support the front end of the lens, taking the weight off the zoom mechanism. I only occasionally shoot freehand and have to be very careful to support the lens with my left hand. Part of my problem (although I love the lens) is that the Sony VCL-HGD1758 is a monster of a lens, weighing in well over a pound. That's a lot of weight to have swinging off an extended plastic tube.
Sony has several variants of this lens and all of the others are much lighter. I don't know how much of the weight saved is by using a plastic case vs. differences in the glass.