Hey @Tom P, thanks for sharing your thoughts on this and happy Monday!
It sounds like you're utilizing a shared folder to do this, in which case all members of the shared folder have to have enough storage space in their Dropbox account to accommodate the share without getting the messages you mentioned.
In that case, you can use shared links to share files or folders with view-only rights which won't be affecting the others and, when you need others to upload to your account, you can use file requests instead.
I hope this clears things up and please let us know if you have anything else to add or ask.