I would suggest if you are considering a DX body to first use the DX mode of your current D750 to get a feel for whether that's even the best route to go. I shot for several years on a DX body (D300) and got decent enough results to print 30X40 (minimal cropping) and 24X36 heavily cropped and resized in Photoshop. The D750 is 10. something mp in DX mode compared to the D300 which was 12. something so for practice with your chosen lens and deciding whether a higher res DX body is worth while will save you some $$. Another way to consider your decision is shooting FF on your D750 and cropping. The end result will be about the same as shooting in DX mode. What you want to do with the final images is a consideration as well. If you are posting online and not printing, you may find the equipment you already own is adequate for bird photography. Rather than spending money on a DX body, solid support- tripod, monopod, window pod, beanbag... may give you better results than a new body.
Final observation is shutter speed makes all the difference! Most of my early bird photos were soft until I started shooting at high shutter speeds. Even though I had to sacrifice ISO for SS it was a worth while trade.
-Chris
