It's been more than a decade since those pictures were taken but as I recall --
What you see in the 3rd pic was done all in one go. I took the soaked leather, sprayed a light coat of 3M adhesive on the cap piece and the backside of the leather and went at it.
It's a tug of war -- stretching, peeling off and refitting, pulling every whichway -- with the heat gun being used as needed.
The adhesive works even if the leather is wet -- possibly not real well but that's okay, you don't want more than a little grip (hence the light coat).
Once I was satisfied with how it was laying on there (3rd pic) I began the folding, cutting and glueing to the inside.