Welcome to the site!

Sounds like you're going in the right direction.

Now, sometimes we reconstruct our memories, including our dreaming ones for many reasons, either to satisfy ourselves because something is missing, or to just put reconstructed pieces in there for the fun of it?

Well, consider dream recall as a muscle that needs to be worked out. Try and set your alarm clock for 4 1/2 hours into sleep then in 90 minute cycles...these are your REM periods for most people.