Back sprite is inconsistent with side sprites when wearing a hat

[melg8]

When you walk sideways you look like so:

As you can see, no red hood visible on that sprite, but when you turn your back, you see red hood:

Which is inconsistent with side view and also looks scuffed.

Possible solution would be:
Add to the CX jar effect giving not only hat, but also "back", which contains hair continuation as on side parts.
(Im not pixel artists, just as rough example):