It's ALL about the lenses. For what you are looking for a lens will cost over $2000. Look at the super-zooms in my previous post. I think that's a better fit for you.
I agree. A bridge camera is probably better suited for the OP’s needs/wants.
The good news is that his budget allows for a very good bridge camera.
And no, I’m not against dslr’s. I own 5 of them and about 40 different lenses. I also make my living with them. I have only 1 lens that has the kind of reach the OP is talking about and it was $3500 (just for the lens).