With your budget, you might be better off getting a Bigma 50-500 instead.
Most of bigma would require recalibration of focusing - then the image would be tad sharp one stop down at the long end. The only draw back is the aperture of 6.3 quite dark for use at the long end. In general >420mm would require one step down to make image sharper.
From your posted image of the balded eagle, the weather seems rather pleasant. This lens would be of use in bright light condition. In dark situation, this lens is not really usable.
Other lenses to consider would be the other sigma zooms 170-400 or 70-300that are comparatively inferior to bigma in general.
Otherwise any A* 300 400 600 would do the job very well or Fa* 300 400 or 600 (if money comes too easily for some people).
Pentax f 1.7X teleconverter comes in handy with some of M lenses and this combination might help as well, the teleconverter about 350-380 US dollars off ebay and M lenses would be less than 900 US dollars in general.
A good quality lens usually can survive some aggressive cropping so some good quality primes 300 or 400mm might be of use if budget is of some issues.
Happy snapping