Mayonnaise has eggs in it so I guess you're basically adding eggs to eggs.
I once took some of the egg whites and whipped them up and then added that to the scrambled eggs. It worked, but it was just too much work to do each time.
The best advice I've seen is to fully scramble the eggs, put lots of butter in the pan on medium heat, and slowly cook the eggs while constantly stirring/mixing them. That way they cook slowly and evenly and you can stop cooking as soon as they are at your preferred level of moistness.
Most cooks say that adding milk or cream actually causes the eggs to “bind”
Not any cooks I know.
My uncle insisted on a little water to keep the proteins loose and the eggs tender. Works well IME.
I think adding any dairy product to eggs ruins their taste.
“Most cooks say that adding milk or cream actually causes the eggs to “bind” which I guess would tend to make them more rubbery.”
I remember when The Frugal Gourmet was on. He said to never use milk or cream — only water. That was for omelettes, so I expect it applies to scrambled eggs, too.
The problem with constantly stirring the eggs, is that they won’t be fluffy. However, if you like the taste of soft (not raw) egg yolk, then stirring them a lot, and plating them while they still look wet, will give you that taste. But it pays to beat the eggs very well before cooking, and also removing that thick blob of egg white that is always present, before cooking, because it doesn’t always cook enough, if you’re making soft scrambled eggs.