Gradiator plugin by Astute Graphics now allows to control all of these, except for specific radial controls (hilite angle and elevation)

Henry, A paid plugin called Gradiator from Astute Graphics now allows to control the center and the length of the gradient (no controls for hilite angle and length yet, but perhaps they will add these later — or probably Ai just doesn’t allow for anything to control it).
This solves the problem of positioning gradient for me, but sure I want live snapping still...

I feel there are many Illustrator tools that lack numeric input like this, which is a shame because those same tools also tend to lack snapping.

A new Gradient is always added to the center of a shape. Moving it is not possible, without changing the size / redraw it.

I would like to move the Gradient within a shape with the same methods that are available for moving other element (numerically, constrain, etc.)

Yogesh, I'm not sure you will get this message until certain time, but I'm glad I can still address this to you.
Yes, user can modify center of gradient. But one can does it only by dragging, with tool, by eye, and not numerically, by typing values, correcting current look by nudging digits and not mouse! I still don't understand why AI, allowing to control everything, takes away some controls.
I personally rarely use modifying center, because I can't repeat same gradient without using dragging.
I need values I can copy/paste.

Add more options to the Gradient tool, especially the radial gradient option. The ability to move the center of the radial gradient would be very useful for cartographers making maps and having the ability to show spheres (3-D circular objects) with a source of light northwest (or any other angle) of the circular object. The attached file should better explain the desired outcome. Your competitors (CorelDraw and Canvas) have had that feature for years, yet Illustrator is more often used for making maps than the other software packages.