Here's the problem:
https://www.flickr.com/photos/902789...posted-public/

Starting from the bottom course, my plan is to use a heat gun to soften
them until they lay flat, then put a bead of roofing cement from a caulk
gun along the bottom edge of the shingle and press it into the one below
while somehow keep weight on it for a hour or so. When I looked at the
cements in my local Ace Hardware store, none said anything about this
use. All the brands mostly mentioned sealing cracks and seams.

Any other suggestions?

Thanks,

R1