Re: how do you manually adjust the exposure correction
Yes, you are correct. It's a little tricky with auto ISO. If we are using auto ISO in Manual (M) Mode and we raise or lower the exposure compensation we are telling the camera to make the picture brighter or darker than what it would normally set it to (with the ISO level). A simple test makes that apparent.
So, with my Canon T7i (800D) camera in Manual (M) Mode I chose 1/250th s.s., F9 and Auto ISO. The exposure compensation was set to 0. The ISO value came out to be 1600 with my test picture. Now to exaggerate it some with this test, I set the exposure compensation to +2. The ISO value was then 8000.
On my Canon T2i (550D) camera I could not do that in Manual (M) Mode with auto ISO. I could not "force" the picture to be darker or brighter than what the camera wanted in that manner with exposure compensation.
I took pictures of the Canon T2i (550D) settings if anyone wants to see them. Instead of lower or raising the exposure compensation (like we can get with the Canon T7i (800D) camera), all we get is AEB bracketing. I'm not sure if that is what the OP is referring to. That's why I suggested a workaround for him or her.
Another workaround is to play around with the ISO levels as you describe and forget about using auto ISO. I would do that also if I knew the lighting would consistently be the same or close to the same. Since I chimp a lot I would raise or lower the ISO value as required (while I kept looking at the images in the LCD screen). At events, I would keep the shutter speed at certain level for the action with a chosen aperture (to control the depth of field). I think I did that at one of the polar plunges.
Thank goodness I don't have to do those workarounds any longer. The newer Canon T7i (800D) camera has been a real blessing.