4mm will be fine, I worked mine out on ampage etc, and think its around 2-3mm thick, but like I said, I have earthed it on both sides, as well as the 4 bolts securing to the gutter rail acting as earths too.

Nice work there I got the exact same bar a week ago so probably wired it at the same time as you

I also used 4mm tri rated, I took my earth down to the engine bay via black mini trunking next to snorkel, must say your wiring looks a bit tidier than mine! I'll sort it out better when it's warmer!