I have all of my figures on plastic bases so I just put sheet magnet in the bottom of my cases.
Magnetic plastic, that's a new one to me

But i was going to suggest similar. either base your figs on (ferro-) metal and transport on magnetic strips
or glue magnetic sheet under your bases and transport in a metal toolbox.

I did it in the past with 28mm figs, worked rather well, but heavy shocks could still toos your figs around.
with 15mm that shouldn't be such a problem.
best solution is mentioned before : K&R or
feldherr (I got a big bag of them and the good thing is the trays are approx. the same size as K&R)