But I’m thinking in hindsight I should have stopped and gone to manual with a higher shutter speed (probably should have been in manual from the start), and shifted to group AF.
Sounds to me like you just experienced one of the best reasons to embrace Manual Mode/Auto ISO shooting as well as BBAF with a secondary AF mode on the PV button or other control. It's situations like that where you start asking what you could do to be ready for sudden changes from static to action or vice versa and how could you set up your camera to swap from one scenario to the other ideally without taking your eye from the viewfinder.
If you run Manual Mode/Auto ISO you don't need a minimum shutter speed setting at all as you'll choose that depending on the scenario and all it takes is a quick spin of the rear control dial to change shutter speed and you can see any changes real time in the viewfinder as you make them. So that takes care of a few things like quickly switching from a perched bird to a flying bird and vice versa and it helps as light levels fall since you can choose slower shutter speeds for more stationary subjects if you see your ISO getting too high or hitting your preset limit and can go as slow as necessary without going into any menus.
The other part is to set up your camera for more than one focus mode. I don't run a D7500 but many of the newer Nikon bodies support this way of shooting. Basically you set up BBAF by setting the camera to AF-C mode all the time with the rear panel AF-ON switch just set to AF-ON and the AF-ON disabled for the main shutter release. That's step one. Step two is to take another easy to reach programmable control button like the PV button on the front of the camera and set it to a chosen AF Area mode that you think you'll use a lot. I set the PV button on my Nikons to Single point AF and its my go to for static subjects, slowly moving subjects or really any subjects where I feel confident keeping that single focus point where I want it (on the eye).
Then you set the main camera AF Area mode to whatever your preferred action setting is. I usually use Group or the smallest Dynamic mode I think I can get away with like D25 or D9 on supporting cameras. You can always change that main camera AF Area mode setting to something else like 3D if that fits your shooting style but I like Group or D25/D9 for most wildlife action scenarios.
So when shooting those perched birds you press the PV button on the front of the camera to select Single point and press the AF-ON button to activate focusing on that single point. If it's a focus then recompose kind of situation because the eye or other main focal point doesn't lie under a focus point in the viewfinder then you let go of the back button once you have focus, recompose and shoot knowing the focus is already locked in. If you can easily place a focus point on top of your subject's eye (or other main interest point) then you just hold both buttons while you shoot to account for any twitchy small head position changes by the subject.
But now the hawks come flying in and all you have to do is forget about that front button and just press the rear panel AF-ON button and you're instantly in your preferred multi point focus area mode (e.g. Group or D25). Yeah, if you've been slowing down shutter speed to minimize ISO then you spin that rear command dial to bump up the shutter speed but everything described can be done with your hands in shooting position and your eye to the viewfinder.
Maybe you're already doing much or all of that but those two camera settings used together can really help when making an instant jump from static to action shots or vice versa with several huge benefits including being able to do it all with your eye on the viewfinder, never having to take your hands out of your most stable shooting and lens holding position, having instant access to two focus area modes and being able to leave your camera in AF-C mode all the time but having the benefit of AF-S mode when it comes to focus then recompose shooting by simply letting your thumb off the AF-ON button after achieving desired focus knowing the camera won't try to focus on its own when you press the shutter release.
I take credit for none of this, Steve has some great videos explaining all this stuff. There are many personal choices you can make when setting this stuff up but based on playing with various modes and experimenting based on feedback on this site what's described above is my current setup. I actually changed one small part in recent days (not having the PV button activate AF while choosing Single point mode) based on ideas posted on these boards and so far I agree it's a slightly slicker way to go.
As with a lot of things, it's a matter of getting used to the process and making it feel second nature so to speak.
