Altium .Designator on Mechanical Layer
This is how I deal with it.

I agree with Krunal in the comments, generally it is not possible.

Every component I make has a .Designator string on a mechanical layer. I size it so that it can fit 3-4 digits within the outline.

Once the design is going into production, I go to the mechanical layer and rotate and re-adjust all the component strings as necessary to create an assembly drawing. I just end up with better results that way, putting a little manual labor into it!