Hmm, definitely haven't heard of anything like that before. You're saying it only happens when storage is full, and stops once you use some resources or construct more storage? If the game is running slowly, does this still happen if you disable shadows and particles, and turn antialiasing off in the Video Settings menu?
I'd definitely be keen to see a log file and some system specs (in particular CPU, RAM, graphics chipset, and VRAM, but a model number should be enough for me to look that up if you're on Apple hardware). If you're able to get a short video, that would be helpful too. Best to send those through via email, since the log contains your home folder path when outputting where it saves games to.