The d7200 is a good upgrade from the d7000. If you can swing it, do that.
The dlsr crop sensor world will be much different than the P900. The advantages are better overall IQ, faster handing, much better for birds in flight. The downside it is much heavier, more expensive, and has much less reach than the P900. The d7xxx + 150-600mm will give you 900mm effective focal length, or just under half the P900 (2000mm optical). With cropping, you can get very good images at maybe 1200 - 1500mm. The d7200 actually has a 1.3x crop mode (so effectively 2x with the 1.5x it already has) and shoot at a faster FPS in that 1.3x mode.
As Niels points out, you will get less depth of field. With a f/6.3 lens, if you shoot f/6.3 - f/8, you should be OK for most birds unless they are large and close. If you search for "dof calculator" you can find various on-line ones to check out the theoretical DoF for a given sensor side, lens focal length, and distance to subject.
You should also get a good sling strap. I used the Black Rapids sling. It attaches to the len's tripod thread and makes carrying the weight much more tolerable.
Marc