Like you, I was never taught to have two layers of fabric when embroidering.
So when I started reading about it, it seemed so foreign.
Yes, I get the reason ... to prevent threads on the back showing through.
But that hasn't been a problem for me.
I guess my Mom taught me well ... the backside should look almost as good as the front.
I try not to jump far with thread.
I did try the two layer method once ...
and found it hard to make sure I got my needle through the two layers.
Instead I try to make sure I use a good heavy cotton ... just a regular quilting fabric though.
As for your muslin ...
I'd try partially drying in the dryer, and finish drying it with the iron and Best Press.