One of the problems I've encountered specifically for storyboarding is that shots, copy, VO, all get shifted around. And when a new shot gets inserted, I have to re-layout everything underneath it. I use Google sheets often for project, asset, and shot management, so I thought that the greatest way to manage the structure of my shots within Indesign, would be if I could do it within Google sheets (where others can help manage, and collaborate on my storyboards).
Is there a way for this to happen, or is there an alternate way to shift things around without having to do it manually each and every time?
There are certainly ways to place data from Google Sheets into InDesign. If all of your content was housed in Google Sheets, and you regularly needed to rebuild stuff programmatically, I might think about suggesting Sheets -> CSV -> InDesign Data Merge. I've set up similar workflows for a wide variety of users. I mention this because setting up workflows is actually one of the things that people pay me to do. You may want to take a look at the Data Merge entry in the help and see if it is likely to be useful to you.
However, I'm not familiar enough with your field, or the way you work, to make any concrete suggestions. You may be building your InDesign files in a way that makes it necessary to, as you say, re-layout everything underneath it. Can you post a concrete example? Can you share a file, then describe a change order to be made to that file that would require you to rebuild or reformat everything after a certain point in the file? I've encountered plenty of creative pros (who are not layout pros - IOW people such as yourself) who are forced by their working style to do lots of unnecessary heavy lifting in InDesign, simply because they've not been doing DTP for 20 years and are unfamiliar with the conventions.