Instructable 8x8x8 LED cube - simpler multiplex ?

I am starting to make a parts order list, for the next project I am going to attempt - the instructable on the 8x8x8 LED cube:

However, when I look at the IC’s on the parts list, I am having trouble finding the following : 8x 74HC574 ICs, 1x 74HC138 IC. Also, as this involves a significant amount of soldering, I am insterested in not only finding alternative parts, but also if I could reduce the component count - perhaps by using fewer, larger, LED driver specific chips.

Obviously changing the hardware COULD have an impact on the software, but may only require some tweaking.

Has anyone done a build based on this project, but with maybe a more streamlined/current component list who could share any advice?
Or, given the info below, suggest a route forward :

Arduino code is here :

Any help would be much appreciated , I am very much looking forward to learning on this project.