Has anyone run into this?
Yes, I also experienced it. After a config reset the host (e.g. 7.12.1) boots with all containers stopped and they won't start until I delete and re-create them manually. What is more, when copying a container in winbox, it misses a remote image, so I must type it myself each time. It is very inconvenient and annoying.
As far as file copying is concerned, I mount folders to containers and use winscp to upload/download files to/from these folders. I have never faced any problems with permissions so far. But I didn't try to copy files from one container to another one, since mounted folders are persistent, i.e. never deleted on container rebuild.