Many people find the 7DII noise levels acceptable, however, I, like you was bothered by it's capabilities in low light and noise levels at ISO values above 800. I am not familiar with noise reduction software, but at least with ACR and/or photoshop, reducing noise results in degraded images comparatively. Hense, I now only use FF cameras. I would venture to say, at least with the 5DIV, I can crop to the magnification of the provided by the 1.6 crop factor(or more) and get great IQ without any noticeable noise. Its an investment but only you can determine whether its worth it.

No, it's not.

I regularly make good, usable prints from images made at ISO 3200, 5000 and 6400 with my pair of 7DII. On rarer occasions, even higher...

Canon 7DII test shot at ISO 16000....



Above was shot RAW and post-processed into JPEG through Lightroom 6 with minimal cropping, slight boost in contrast, and only the software's default levels of noise reduction and sharpening applied. I took a lot of care to avoid any under-exposure... no increase in image brightness was needed.

With any digital camera, to minimize noise issues I think the keys are:

1. Avoid underexposure.... if you have to boost exposure in post-processing, it will greatly amplify noise. ETTR is one technique used to help avoid underexposure.
2. Fill your viewfinder with your subject.... minimize cropping. Above image detail on the right is probably close to "100%", and noise begins to show. It will with any camera (though it's pretty well controlled in the above example).
3. Use proper work flow.... noise reduction should be applied early in the process, before resizing the image... and especially before sharpening, which should be one of the very last steps (well after any re-sizing is done). Also take care not to over-sharpen, because that will also amplify the appearance of noise.
4. Be realistic.... Looking at a 7DII's image "at 100%" on your computer monitor is like making a three by five foot wide print, then viewing it from 18 or 20" away! Of course it looks like crap! (Same effect as over-cropping an image.) Sure, it's fine to zoom in to high magnifications for retouching work.... But, when evaluating images for noise, focus accuracy, sharpness, etc., back off to a more reasonable and sensible magnification. View the image at a size close to your intended use of the image (even then, a computer monitor rendition is nowhere near as sharp and fine as a quality print will be... even the best monitors also clip the dynamic range of images, too. I.e., there's more detail in shadows and highlights of a quality print, than you'll see on-screen.)
5. For super high ISOs, it may help to use additional noise reduction... I use a Noiseware plug-in with Photoshop (also available as a stand-alone software, if not a Photoshop user). But I think even Lightroom 6 does a pretty good job.

I shoot a lot of action, rarely use my 7DIIs below ISO 400, use them freely up to ISO 3200 and occasionally even higher than that with added post-processing noise reduction, when necessary.

Hello MS Donna, You say you shoot birds in flight. The 7D mk2 is one of the best cameras made for that particular requirement. The focus tracking system on that model is superb for that purpose.
Check it is the camera producing the noise and not your editing software. When I first had my 7D (the early model) I was a little disappointed there was some noise in my images. Some time later I discovered the Canon software supplied produced far less noise than the Camera Raw software I was using. Camera Raw had more user friendly facilities and more of them than the Canon software. I would have been better served by using the Canon software and then moving the images over to Camera Raw. Now, of course that has been fixed.
Imagenomic Noiseware is a fabulous programme for correcting noise problems.

I use a 7DII quite a bit. I overexpose my pictures by about 1/3 to 1/2 of a stop. It's called shooting TTR (to the right). That will cut down on a lot of the noise. Also, try to keep your ISO at 400 or less. Noise is at is worst when a photo is somewhat underexposed. Also the shadows and dark areas show the heaviest amount of noise. If you can shoot with your ISO around 100 or 200, you'll notice a big improvement.

The software that I often use to help reduce noise is Topaz DeNoise 6. I ordered it online, and it is a plug in with Photoshop CC 2017. Topaz DeNoise 6 can also be use by itself, as a stand alone program (separate from Photoshop). I load my photos from my camera into Lightroom directly off of my compact flash card, and I really like the noise reduction program that Lightroom offers. If I don't get the results I desire from Lightroom, then I send my photos to Topaz DeNoise 6. After all the above is done, I send my images to Photoshop for any finishing up work that is necessary.