At work, I have a lot of processes that have to be developed and then automated and figured I might be able to offer some advice on automation based on personal experience.

My basic rule is to start out with a manual process and automate as you get the process working. When you try to build in all the automation before you even start, one little flaw in the design can sometimes cause a big disaster and it's a lot harder to figure out what is causing the problem.

In this scenario, is there a way to advance the projector manually and does the camera have a remote or cable that will let you take the photo manually without having to press a button on the camera itself and potentially cause it to shake? If so, start by building a setup that lets you manually advance the frame and then manually take the photo. After that, start looking for single steps you can take to automate. Is there a way to make the projector automatically advance one frame after you take each photo? If this works, then you can look at ways to make the camera take another photo after the frame advances or take photos at the right speed to catch each frame.

This is just my two cents. Hopefully, it will help.