Right, the D610 with crop-frame lenses would essentially be a 10MP crop-frame camera.
What do you find the limitations / difficulties of the D3400 are?
Depending on your needs, it could be a better investment to get higher-quality (ideally full-frame compatible) lenses rather than a body upgrade. Of course that would mean you still only have one camera, so only one person can use it at a time.
My initial response would be that the D7200 would probably be best for you, and wait a few years until you can afford the full-frame lenses and eventually step up to the D780 or whatever it is at that time.
D7200 vs D7500… The D7200 has two card slots and slightly more MP, which means slightly worse high ISO performance at a pixel level. Probably you can get a better deal on the slightly older camera.
A note on comparing noise with the D610 using those photos… In those photos the D7200 and D7500 are using an ISO of 25600 and the D610 is using an ISO of “High 2” equivalent of 25600, which means it has been digitally boosted 2 stops. Also, the shutter speed, aperature, focal length, and lens are not the same between cameras, making it a bit of a difficult comparisson. You will probably never use anything over ISO 6400 anyhow, except in tests or in pictures you aren’t going to keep.