Thank you for your appreciation! We are all learning, and I shall learn from your situation too.
If you need to be able to get to 400ft, then you definitely want more reach than the 70-200 is going to offer, even with the boosting effect of a crop sensor. The compromise for that sensor magnification loss is that you will be using super telephoto lenses and having to accept that such lenses are relatively slow, and given you said that is a challenge for you, we need to find a solution that will alleviate that. This is where my suggestion of going full-frame comes into play.
Any APS-C sensor camera, compared to a FF camera with the same pixel value is going to perform worse in low light. That is because the photosites, the light-gathering components in the sensor are smaller and more prone to noise. The R7 has squeezed 32MP into its APS-C sensor which, if translated to the same density on a FF sensor, would be 83MP - which no camera maker has successfully achieved. The results show up clearly in the tests of sensor performance in terms of ISO and dynamic range.
See the chart below from a site called Photons to Photos, that geeks out on camera technology:
The table represents the maximum ISO value that each camera could use to achieve a dynamic range of 6.5 stops. The R7 is second from the poorest, while the the R6MkII is over twice as effective and just above the boxed around the R5. There are also issues with the readout from the sensor at high frame rates, and bottlenecks throughout the data bus. If you don't shoot high frame rates or shutter speed it might not be an issue, but the mechanical shutter sounds like a tinker's cart, which drives most people to use electronic shutter, which is where some of the issues start.
I would suggest that you can still do this in under your $3500 budget. So, with all that in mind I am suggesting you sell the R7 to help fund a FF body - better now that at Christmas when you are competing with the big sales. Yes, you will lose the magnification boost of the APS-C cropped Field of View, but you will gain significantly in terms of focus, dynamic range, and face/eye tracking. I would recommend replacing it with the 24MP FF R6MkII - it is currently bested only by the R1 and R5 in terms of focus, and they are significantly more expensive. You can use your current batteries and cards so that should be painless. There is a slight difference in controls but you can get used to that. The R6II refurb at a cost of $1,699 has been reduced again.
Now to Optics:
Having improved your DR and focus, consider one of the following:
The Sigma 60-600s lens for Canon - you could get this from KEH.com. There is none available right now, but you could expect to pay around $1,600 for a like new one - with a warranty. That is an awesome lens - not light, but you can use it with a monopod very effectively from close far. That, taken with the quality of the sensor, will allow you to crop if need be, but you will get good light performance because you can boost the ISO to something like 6400 - far better than you are doing right now.
Alternatively, if you can find one, consider the RF 200-800 f/6.3-9. Canon have it listed at $1,899. I have this lens and for the price, it is an amazing performer. To compare the fields of view between the setup you have now and this one:
With the R7 equivalent: the 100-400 f/5.6-8 will render a FoV equivalent to lens160-640mm f/8-11
With the R6II you will get the 200-800 will give you the same native range, but you are now gaining an effective aperture benefit of 1 stop over the other lens - and it's a fabulous optic and has IS that will work with the far superior IBIS of the R6II.
So, if you were to sell the R7, you can keep the 100-400, get the R6II and RF 200-800 and should still stay within the $3500 budget.
As to your settings.
I think I would be correct in saying that a lot of photographers for sports still shoot in Av mode. Consider for every shot you have 3 variables to deal with, but you are dealing with a dynamic situation, so you want to cut those down as much as possible, so I use the following and it works with animals that don't cooperate.
ISO - set to auto, with an auto range up to 3200 or 6400 - start low and see how that works
Av mode, so the camera is sorting out the shutter speed, but again you can set parameters for that
Now all you have to do is deal with aperture, keep an eye on the S/Speed in the viewfinder and track.
If you have not done so, I recommend using Back Button focus, single point centre focus, in Servo mode using the default AF-On button on the back. I also set the exposure to single point, centred and have that set via the * button on the back.
See: https://www.youtube.com/watch?v=2AXUzslHnRc&t=2s
Metering: Evaluative metering tries to average out the exposure, but often in contrasty situations that will not work well and you don't want to spend time using the EV dial to compensate. You don't want the exposure linked to the focus point because there is no guarantee that this is rendering an18% reflectance that the sensor wants.
So, the process is:
Centre the EVF on a point that has moderate balance between light and dark - it comes easy with experience - and TAP the * button to lock that: a * appear in the EVF to confirm. If you want to change, point at the new place and tap the * again.
Centre the EVF on the subject's face. With face and eye tracking enabled it may find it, but centring on the subject's face/eye and tapping the AF-ON button will confirm that to the focusing system and it should take over tracking. If the focus point is not on the centre to start with, tap the joy stick to centre it (if it is not set to do so, you can configure that in the menu).
Recompose and shoot.
It actually sounds a lot more complicated than it actually is, and it is lightning fast once you get enough practise in - far faster than moving the joystick, for example. I don't use touch focus as my face keeps touching the screen and confusing it.
Aprice2016,
To piggyback on what Trevor has conveyed the 100-400mm on an APS-C camera should allow you to capture some nice if not beautiful images.
Just so you have some point of comparison the image below was shot with a R6 MkII and the RF100-500mm F4.5-7.1 L IS USM lens. It was taken from left/center field behind the home run fence. The settings were ISO 2000 - f8 @ 1/3200 - focal length/zoom 383mm on an overcast day as you can see, the players have no shadows.
The reach of your RF100-400 equivalent field of view of 160-640mm would allow you to achieve a very similar composition. The RF100-400 is also the lightest of the three lenses I mentioned coming in at 1.4 lbs, the 70-200mm - 2.36 lbs and the 100-500mm - 3.0 lbs.
One other consideration you may want to think about is using Auto ISO and setting you aperture and shutter speed manually.
