For what you want and in keeping within your budget, I agree with the members who’ve recommended the first generation Tamron 150-600. I had one which I used on my D5200 and D7200. When I bought my D500, I sold the 1st generation lens and bought the G2. In hindsight, I wish I’d kept my 1st one. At least I sold it to a friend and she really enjoys shooting with it.
MadMikeOne, why do you regret getting the newer version of the lens? I recently purchased a D500 and was thinking about doing the same thing you did.