Regarding just this one point of your post . . .
I had been looking at the designs of an offset scalar for C-band, recently.
Yes, I believe the tips of the rings do form a cone which includes an angle just big enough to see the dish.
And, given a round set of scalar rings, the dish must appear round from the perspective of the LNB.
For typical offset dishes, that makes them a little taller than wide, and their aperture is the width,
not height, of the dish.
So, if your dish is 30" wide and 36" tall, it's not really a 36" dish, it's a 30! -

This is not in keeping with the way imported dishes are measured, but if you compare their performance with commercial dishes, I think the answers will be clear.
Now, as to the scalar spacing...
The only document I could find, suggested scalar rings be spaced no less than 1/4 wavelength apart, and no more than 1/2 wavelength.
The same measurement applied to their height.
Measuring ring height in an offset scalar wasn't clearly documented.
Hope you can confirm the info on the scalars.
Working at Ku sizes will probably require considerable care and accuracy.
C-band on the other hand, is something I'd be a lot more comfortable dealing with.