Correct knockdown texture

There is a large ceiling with a knockdown drywall texture. It is very uneven in the size of the high spots, the scene of the paint, the amount of relief, just about everything that could be wrong with a knockdown. The owner wants it corrected. The only way I know to fix this is to skim the whole lid to flat then retexture. This will be expensive and hard n my shoulder. Has anyone had success re spraying and knockdown over previously textured and painted knockdown without making it smooth again?
This will be a paying job and I want it to turn out right.

Correct knockdown texture