The 70-300 F4.5 is 5.6 at 300mm. This F5.6 lens with a 1.4 TC will be F8 at 300mm, making the focus performance challenging at best, and you can just about forget about using it in poor light (early/late in the day, under the forest canopy, etc). The D750 has only 15 cross-type sensors which can work with a lens with a max aperture of F8.

A 300mm lens will be 420mm, regardless of sensor size. Cropping will simulate longer "reach" whether you do it in/with the camera. Getting a crop sensor camera will put more pixels on the subject, but the larger pixels on the D750 will provide better sharpness and light-gathering capability. Uncropped images taken with a D500 will not look as good as cropped images taken with the D750. I did a similar comparison with a D500 and a D810, and the D810 won each time.

A third party lens is not automatically a candidate for fine tuning. in fact, third party lenses often perform on par and in some cases even better than the OEM lenses. I chose a Sigma Sport, which I purchase used in 2016 for $1100, over a brand new Nikon 200-500 after borrowing 2 copies on separate occasions from Nikon's NPS program. The Sigma was noticably sharper, even though I fine-tuned the Nikons. I am not saying the Nikon lens it bad. I am saying that the Sigma was simply and visibly sharper.

Case in point, the shots below were taken with a Sigma 100-300 or a 150-600, straight out of the box - no fine tuning, and all are moderately to heavily cropped:

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I started birding with a Tamron 150-600mm f/5-6.3 G2 on a D7200. I was not getting good results beyond 400mm so after "talking" to Customer Service I sent the camera and G2 to Tamron where they found no problems with either and they came back no better than they went out. I thought I had wasted my money on the G2. After a lot of research, I learned how to tune using Tamron's Tap-in and with a lot of time and effort I started getting good results with the G2 even at 600mm (which is not really 600mm, it's more like 550mm).

Along they way I picked up a used D500 and found I did not need to re-tune the G2 to the new body, they worked just fine together and still do today. I picked up a Nikon D200-500mm f5.6 and found the Tamron and Nikon had similar IQ in the center, but the Nikon was sharper towards the edges and much sharper in the corners compared to the G2. The Nikon focuses much faster than the G2 at longer focal lengths, probably the difference between f/5.6 and f/6.3. I can also use a 1.4x teleconverter with the Nikon, which takes me to 280-700mm f/8 (420-1050mm f/8 on an aps-c body), and the AF on the D500 (and now my D850) work fine at f/8 as long as I use the center of the frame (BBF really helps here), but AF is slower at f/8. I go to manual focus under lower light conditions.

So, my recommendation is to stay with Nikon glass for these longer focal length zooms. With that said, I am getting very good results with Tamron's shorter zooms, especially the 24-70mm f/2.8 G2, 70-200mm f/2.8 G2 (rarely comes off my D850) and their 35mm and 85mm f/1.8 primes.