Altium propose the functionality "Align face to board" for 3D body placement. When you click on this menu option, you can click with the mose to select the polygon of you 3D body that needs to be aligned with footprint copper.
Adding such functionnality can make placing 3D bodies really easier than having to fiddle with Z placement.
Add 3D body alignment to board
Re: Add 3D body alignment to board
Thank you for offer. Now we don't plan to implement this.