Two answers to your question.
Part one: given where you are, the next step up would be a Panasonic (or perhaps Olympus?) m43 camera with the panasonic 100-300 lens. It will not give you quite the reach as maximum on the FZ80, but it will give you the same reach as the 30x zoom you say you are able to use. Considering the larger sensor you should be able to crop a little more afterwards and get the reach you need. The lens is about $500 (if you want, you can upgrade to a better 100-400 when you get the money), and you can get cameras (even if they are yesteryears model) within your total budget. This should not be too much heavier than your current setup.
Part two: are you sure you have used the camera you have now to its fullest? you did not show the image you complained about and do not say under which conditions/settings you have that problem. One of the problems with the current camera is that the lens become gradually darker as you zoom, and if you have a short shutter speed, you get high iso which leads to that effect. However, you should be able to not see that in good light, and even in poor light, some good postprocessing can improve a lot if you are shooting raw. The images you show are good enough that I would not give up on the camera without trying further. (in fairness, the lens becoming relatively darker with zooming is true for most budget lenses, you would pay thousands of dollars for one that does not do that).
Niels