This is likely a media issue. Potentially some high res stills, those photo jepgs, or another piece of media that failed to properly “ingest” during the creation of the project file or a sequence.
Also encode those MOV photo/jpegs to pro res.
The problem also sounds like the media cache database and cache location. Where are the machines pointing for that?
I know you said you have already attempted that but keep in mind that “cleaning” the cache will only remove items not currently used in the open project so its best to do with no project open or a test project open.
I have had more success doing it manually and rebooting.
Is the machine still generating .pek files during this “lag”?
Check the video previews location in the project settings too.
You can try to point the previews to the local internal ssd of a problem machine, delete the render files and re-render to prores previews. If this solves the issue then you know its the “render” location.
In your setup you will probably want that pointing to a local drive or the server but NOT one of the other edit machines.