Hi, never won a demon either, I just went once and got a finalist pin but I also do local competitions when I got the time.
On my side, I've tried multiple things, most revolve around "patafix" (french stuff) which is the equivalent to blue tack i guess.
I usually put some under the base (or plinth) and then some on the sides to try and "grab" the base (or plinth) so it's secured pretty tightly.
Then for transport, I repurposed a wooden box for wine. Its size is kinda big but it does the job.
I avoid foam and anything that would touch my miniatures because I'm afraid it's going to grind the paint away.
For the GD the box was too big to fit simply on the plane so I used a jar.. Not such a great idea, I had a lot of trouble explaining to the guys at the security check out (ended up missing my plane cause it took so long)