I keep breaking needles when felting a very thick felt mat

I have made some needlefelting projects previously, and haven't had major issues breaking needles, but I've started a project that is the bane of my needles:

It's basically a custom playmat for a boardgame, with space for 15 cards and a little pouch for each, so they don't slide on the mat. The pouches will be made from regular cloth, but I want to felt on little details.

I've bought a very dense woolen felt mat, 5 mm thick. I've tried to felt on some details, so far using thin synthetic felt-mats (as a coloured base), and even going really, really slowly, I've lost four needles in four minutes. When I push the needle down in the mat, there's just so much resistance. I've tried to google if you simply can't felt in so dense a material, but I just keep getting generic results on how to not break your needles.

Does anyone have any experience felting like this? Or any tips on how to proceed?