I just bought a large sheet of spongy rubber. I think the guy in the shop called it PVA, but there's no label or anything on it to confirm that. My intention is to cut it to size and shape and use at to 'soften' the desk for the entire length of both my arms. Again, I'm not certain that this will 'solve' the problem, but I think it will help.
The gel palm rest was too tall, made me bend my wrist awkwardly, and transferred the desk contact pressure to my elbow.
The 4mm mouse mat reduces the pain, but also shifts a lot of the desk contact pressure to my elbow.
In theory, having my entire arm supported on something with a bit of softness to it will avoid the elbow issue, while still reducing the pain in my hand/palm. I dare say further refinements will happen after that.