I'm about to give up on Maya because of skinning.

Okay, I'm not an expert, but skinning seems fairly straightforward to me. However, one thing I do know, it can't handle all rigging situations or all poses.

I wonder if blend shapes might be what you need?

Have you learned anything about Maya blend shapes yet? Blend shapes are basically morphed duplicates of your original mesh. You duplicate the original mesh, then you push vertices around to reshape it any way you like (though you cannot add or delete vertices nor change the basic topology). Maya is then set to blend between the different blend shapes (morphing, morph targets). This allows for much more sophisticated deformations of your shape then the weight-painting of skins allows.

For example, here is a video on corrective blend shapes. I bet that's what you need.

There's many blend shape tutorials on Youtube to help you out. Paid video courses too.

It's most often used for facial rigging, so emotional expressions move nicely, though it can be used anywhere that mere weight-painting of skins doesn't give enough control.

For example, the Morpheus rig uses multiple blendshapes extensively for the entire body, which is what allows you to morph the appearance from female to male, from fat to muscular to skinny to curvy and everywhere in-between.

There is also Maya Muscles, which allows a more subtle and realistic deformation in response to bending, twisting, and unbending, though this is considered an "advanced" technique not used in most rigs I've seen.

Sometimes the rig itself could use an extra bone here and there, to help maintain the shape and volume better in various poses.

/r/Maya Thread