@Sootchucker
First of all, I'm a bit of a long tele freak and do 99% of my shooting hand held. Since my Nikon days, I've owned or still own Nikon 300mm F4 AF-D, Tamron 150-600mm G1, Sigma 150-600mm Sport, Sigma 120-300mm f2.8 Sport with both TCs, Sigma 100-400mm, Nikon 200-500mm, Nikon 300mm f2.8 AF-S II. I've also tested the Sigma 150-600mm Contemporary and Sigma 60-600mm.
If we're talking about comfortably hand holding a tele lens, you have limited options...300mm F4 (AF-S or PF), 500mm F5.6 PF and the Sigma or Tamron 100-400mm. I can say that I was impressed by the quality of my Sigma at the tele end wide open. It's definitely something you can put inside a bag in case the need arises.
With the other lenses, I've gone through the entire day carrying them around and you'll be sore at the end of the day. I loved the IQ of the 120-300 bare, but the 2x TC left something to be desired. The lens had some issues with AF-C tracking as well. Since I need 300mm+ focal length more, I sold the Sigma and bought the Nikon 200-500mm, which won the head to head contest with the Sigma 60-600mm.
I also acquired a Nikon 300mm f2.8 AF-S II a few days ago since the 300/2.8 look of the photos haunted me. I will test it with the Nikon 2xTC in the next week when I receive it (the TC, the lensI already have).
In regards to your issue. I would suggest that the ultimate portable hand holdable tele kit would probably be 70-200mm f2.8, 500mm f5.6 PF and the 1.4x TC.
But barring that, I'd say that getting a D500 won't really help your issue...you won't put any more pixels on the subject than with your Z7...the AF might be better on the D500, but I would say that might only apply if you're chasing small garden birds...anything else I'm not sure the difference would be a game changer. Your Z7 + 300 PF + 1.4xTC give you a very respectable 420/5.6 or a DX 630/5.6
Getting a Nikon 200-500, won't be difference enough...80mm more won't make a difference. One of the 600mm zooms...you'll start seeing a difference in subject magnification, but they're heavy and clumsy (especially the Sigmas).
Here's a thought....wait for the 200-600mm Z lens from Nikon, add a D7200 in the mean time to your setup (half the price of the D500 and more megapixels).
Sorry for the long post, but you posted about my favourite two subjects, long lenses and gear shuffling
