especially because it looks like the cubes are not uniform in shape

The image is deceptive. The cubes are uniform, and the "fins" are angled to beging with, and the lever straightens them, which ejects the cubes.

This image might give you a better idea:

But the cubes aren't PERFECT in their shape, so if that bothers you, then there's no way around it with this style of tray.

I think it probably would be possible to make an ice cube tray in the twist style out of metal, if it was a relatively flexible metal.

Yes, I think that would be possible, but you'll likely end up with fractured cubes. Silicone trays are the best for perfect cubes, but they make the ice taste bad.

Good luck in your search!