I was lucky to have the manual in my glove box when I got my LJ. However, I still folded it just like you did on first go and that was WITH the manual. I didn't have the strap though.
It's more 'natural' to have the fold forward, but evidently that's not how it's designed.
I've driven it open, fabric to the rear, without the header strapped down and it doesn't seep into the cab.
(FWIW, I wanted a strap too, so I bought a too-short strap on Quadratec for the hardware, then sewed my own strap with that hardware. Link:
https://wranglertjforum.com/threads/got-an-email-from-bestop.67509/post-1251482)