I am not a fan of the 18-400. All the reviews I have read say it is just ok or soft at the long end, effectively making it an 18-300 or 18-200, depending on how much image quality you want to retain. The D500 is a great camera, but you are going to lose about 3 mp of resolution going from the D3300 to the D500. What you will get is a "Mini D5" with outstanding handling, large, bright viewfinder, better dynamic range, more accurate focusing, etc etc etc. You'll love it. It would be a shame to pair it up with consumer grade lenses targeted at casual users looking for convenience rather than image quality, which is who most 15x to 22x zoom lenses are supposed to be for. Too many image quality compromises for me. However, I think that the 18-200 is a pretty decent lens, again, at less than full zoom.

So if you want to get to 400mm or longer, I would suggest a used Tamron G2 150-600, or a used Sigma Sport 150-600. If you get a used, but good condition D500, you will be well inside of your $3000 budget, and you will get some spectacular glass to go with a nice, pro-level body.

However, it was my money, I would bypass the D500 altogether and get a used D810, or even a D800. You won't believe your eyes how crisp a 36 mp image can be, especially with good lenses. I just posted a few shots taken with the Sigma Sport and a D800 and D810 in this thread:

https://www.uglyhedgehog.com/t-584589-1.html

The D500 body is currently going for $1799.00 and the Sigma Sport 150-600 is going for $989.00 That makes your total $2788.00, and you'll have a great package for wildlife. I suggest this because you already have a couple decent lenses to cover everything under 150mm. And you can pickup a use or refurb Sigman 11-16 fairly cheaply. That would keep your total expenditure pretty close to $3K. I think you may find that 18-400 to be just a little short for wildlife and birds. It's a great lens, though.