This is beyond Photoshop Scripting.
If not, is it possible to create an alternate layer pallet using scripting or plugins?
It might be possible to create a custom Panel (possibly with Flash Builder) but I doubt that this is advisable with regard to performance etc.
Yes, it is absolutely possible.
So long as each button on the layers panel is associated with its own keyboard shortcut, then this can be done easily.
With Autohotkey, you can create your own toolbars and place them anywhere on the Photoshop screen. Each button you create will have its own icon image (.bmp for example), and when clicked on, will send its keyboard shortcut to Photoshop.
If you want to add a 'new layer' button to your new custom toolbar, you just create your own little .bmp image of new layer (whatever you want it to look like, maybe a red '+' sign), then program the button to send 'ctrl/shift/n' to photoshop, and it will add a new layer to Photoshop whenever you click this button. This allows you to ignore the default 'new layer' button that's on the bottom of the layer panel and instead use your own custom button. You can have this button appear anywhere on your photoshop screen; it allows you to drag it anywhere on the screen. You can add unlimited buttons wiht unlimited keyboard shortcuts to your custom toolbar and have it look anyway you wish - you design it.