I'd suggest you rent (e.g. LensRentals.com, BorrlowLenses.com, etc.) a 7D II and a 5D III ... and compare them by shooting a game. You may even have a local camera shop that would rent gear. That will help you decide and you won't have buyer's remorse. I suspect you'll be quite happy with the 7D II... technically a 5D III will outperform at high ISO.
As for noise... I use this software less and less (since my 5D III and 5D IV shoot clean enough that I seldom need it) but my favorite software for dealing with noise was a photoshop plug-in called Noiseware Pro by Imagenomic. The reason I like this particular noise reduction software is because I can adjust how aggressive it will de-noise the image based on tonality. You'll typically see heavier noise in darker areas... and much less noise in lighter areas. The software lets me analyze the noise (and it'll auto-apply an adjustment) but then I can go in to the controls and adjust the noise by tonality so that I don't apply too much de-noising in areas that don't really need it (if you apply too much de-noise then skin starts to look like plastic.)
Another piece of software is Nik Define 2. The Nik collection is now free. You can download and install it (it also comes as a Photoshop plug-in) then use Define to analyze and apply noise reduction. Define lets you drop small boxes to make it sample noise in various areas and it also applies some auto-reduction... which you can also tune. BUT... another cool feature of Define is that you can also use a "brush" option. This actually creates a new photoshop noise reduction layer with a layer mask and you use a "brush" to brush-out the noise where you think it's a problem ... rather than just applying some global reduction across the whole image.
One nice thing about the "brush" choice is that noise reduction tends to soften edges... so this would let you "brush" on the noise reduction in the trouble spots... but stay away from the edges where you want to maintain good detail.
There's also a way to do this with just Photoshop alone (no plug-ins -- but requires Photoshop CC ... my older versions can't do it). This involves duplicating the background layer, aggressively de-noising that layer, but then creating a mask on that layer so that not all of the de-noising is applied. You can then do an "Image" -> "Apply Image" (but tick the "invert" box) and this creates what looks like a black & white negative of your photo in the mask. The reason that's cool is because if an area of a mask is "white" then any change made in that layer is fully applied. If an area of a mask is "black" then none of it is applied. But if an area is "grey" then it is partially applied depending on how dark or light the gray is. The effect is that this causes aggressive noise reduction in the darks (where the noise is always the worst) and little to no noise reduction in the lights (where noise typically isn't visible.) You can also "brush" selective parts of the mask darker or lighter to increase or decrease noise in that area with more control.