You're right, renaming the groups without spaces fixed it, thanks!
In fact I don't even have to change the actual name of each domain group, just its pre-Win2000 name (as the latter field is what the ReadyNAS sees and validates). I was a bit hesitant to rename the NT built-in groups such as 'Domain Users' and 'Domain Admins' though.
Funny thing is, I can rename these groups back to have spaces in their names afterwards, and the ReadyNAS will automatically
change the share folder group field to reflect the change. So this is a workaround