Good to know my ideas aren't too crazy!
My reasoning for the order of the math operators may be odd, but it went like this:
Add and subtract are simpler constructs than multiply and divide so I put them first. And, to me, addition is easier for young kids to comprehend then subtraction so I put the addition first. To be consistent, that makes multiplication come before division. Now, my view on these things may not be accurate, but they don't have to be. They merely have to match how I think of them since it is to help me remember where they are, not someone else!
I didn't set the extra symbols on the green layer with a lot of thought - at least not enough thought to remember why for most of them! Looking at it now, the top row is a mirror image of the normal home row green layer on the left (had to move it up because the math operators are more important to have on the home row).
On the bottom row, I figured parenthesis is common enough that it would be best to have them under the index finger. The power of and square root seem related to me, like addition and subtraction are, so I put then next to each other. Having room for another on the green layer, I just stuck the "?" in there.
You list of various ctrl and alt key combos is very interesting because they are things I never really got into, so never used, which means I didn't even remember they exist! I may have to look at using some of them, since it is so much easier with customization. But I'll need to see which ones work with Numbers. I have Excel on the Mac and iOS, but I really don't use it. Some of yours don't seem to work with Numbers - though maybe there are alternatives. Only checked the first two. ctrl-D and Ctrl-R don't seem to do anything on my Mac. So I have some experimenting and research to do on these things.
As for organization, that can be tough. Ctrl-D and R seem related to me so I'd naturally have them connected in some way. Formatting numbers for the most part might be best to leave in default positions on the home row. You don't have room for the ^ symbol, but right off the top of my head, I'd probably put it on the T key. I mean, it is still grouped logically and the ^ symbol looks like an upward arrowhead so I put it "up" above the rest. Alternative would be to put it on the home key on the far left if you really wanted them in the same row.
No idea yet how I'd do the rest.