Again many uncorroborated "opinions" which cherry pick the obvious positive attributes of using a crop DX sensor on FX glass. Which is grossly misleading since it sweeps the negative attributes aside.
"...I have shot the Nikon 500 5.6 PF lens off the D500 with great results..." Really BillNikon? Show me just how great your claimed results are... Besides with OP is shooting the AF-S 28-300mm f/3.5-5.6G VR optic not the Nikon 500 5.6 PF lens which has a price tag of $3,596.95... virtually four times greater than the OP's lens.
No you like the other posters here are pontificating without documentation of your claims.
The kayak image is another real world example that showcase exactly what the OP's lens is capable of shot on FX.
Important Note: The 800lb gorilla in this mix is "Subject Isolation" inherent with FX glass shot on FX bodies.
The Soccer goalie image below is what a Nikon D3 (an equivalent sports camera to the OP's D500) can achieve.
You will never likely see that level on dreamlike Bokeh from a DX body, period!.
I stand totally behind anyone who understands the merits of shooting FX glass on FX bodies.
And all the arm-waving and pontification in the world will not change the outcome of the results .
Go ahead and shoot an f2.8 lens on a DX body and you just turned it into an f4 optic (if that works for you fine, it doesn't work for me). Also the reduced size of the DX viewfinder doesn't lend itself to capturing the "Decisive Moment" DX cameras are more like "toys" not tools for use by commercial shooters.
While I accept that the D500 is a viable tool for use by sports shooters, much of that goes to it's superb AF system. It wasn't until Nikon released their mirrorless FX cameras did a viable alternative to the D500 exist
So limitations aside, the D500 can indeed be a useful tool for a commercial sports shooter... Totally agree here.
Final Note: cmc4214 post is likely the most germane and appropriate in this UHH thread.
"Here is a link to Steve Perry's web site, he has some very good info on setting up auto-focus for Nikon
https://backcountrygallery.com/category/nikon-gear/ I hope this helps
The OP's issue most likely is a want of expertise...
Food for thought: Photographic Excellence is not a consumer commodity.
It only comes with blood, sweat and tears from a long epic struggle to master the craft.