Thanks everyone for your input.
The stubby coolers, of which we seem to have many....work a treat on so many things. I have taken the bottoms out of them and tuck them into the door pocket in our car. Keeps my glasses, hand held radio, sunscreen, bushmans etc handy upright and not rattling!
I have also wrapped items in the non slip mat with rubber bands.
It seems that the trick is to keep them tightly packed. But I will definitely do the extra plastic bag as a precaution.
Thanks again.