I think there’s only one good way to attach any laminate or veneer.

Contact Cement.

Basically, you’d lay out the door horizontally, and prepare the surface then apply the cement to the door.

then you lay thin strips of wood, that run the full width of the door, down at relatively regular intervals.

then you apply the cement to the back of the laminate (cut to slightly larger than you need so you don’t have to worry about exact positioning)

then you lay the laminate sheet down on the spacers and adjust as needed to position (it only sticks cement to cement, that’s why you have the spacers there. Then, once everything is in place, you start removing the strips, usually from the center out, so the two cenemnt surfaces come inf contact with each other and instantly bond (there’s no adjusting at this point) and you continue until it’s all out flat, then you trim the edges with a router.