I made a set of mud flaps for my car using the black foam board used by sign makers. It's very easy to cut, stiff so it sits exactly the shape the original mud flaps were designed to sit without any support brackets like the original ones used and looks like the original mud flaps to the casual onlooker. I used 3 mm thick and found it strong enough but you can get thicker material if you wish.
I made mine about a inch or so shorter then the originals to help them blend in a bit more.
You could use the same material for your 'engine bay mud shields' too.