There are two separate topics in your description:

Currently, axis3d.Axis inherits from axis.XAxis

This is the awkward part. axis3d.Axis is basically monkey-patched on top of XAxis ("take what works for a special case and add 3d 3D functionality and make it the tempate for all concrete 3d Axis). Basically, what you need to do is

1. Copy axis.XAxis to axis3d.AxisBase let axis3d.Axis inherit from that. This already decouples the 3d stuff from concrete axis.XAxis.
2. Go through all functions and decide whether they are (i) needed as is in 3d (ii) should be implemented differently in 3d (iii) are not needed at all
3. For each function, decide whether it could be pushed to axis3d.Axis or it's subclasses axis3d.XYZAxis.
4. Eventually axis3d.AxisBase should be empty again and can be removed.

There's a lot of footwork in this and you may decide to leave some things untidied, e.g. _init() takes some rcParams from the direction-dependent rcParam variants. Since all 3d Axis inherit from XAxis they all currently use the 'x' axis rcParams. Changing that would be a backward-compatibility issue and if at all should be investigated later.

Rename axis3d.Axis to Axis3D.

I would not do this right now. It's slightly inconvenient/confusing to have the same class name twice, but they are clearly separated through namespaces.