Those who are asking for an unlimited free version aren't likely to convert into paying customers so disregard them.
The actual premise of the freemium model is that users will convert into customers once they reach the ceiling of the allowed capacity (the number of projects/contacts/collaborators/tasks/etc). It also allows to test drive the product without fully committing to it (i.e. roll out a small pilot).
When you have a limited-time trial of the full-featured offering, you're already covering both of those points. The time limit forces users to convert or abandon the product quickly while the complete product allows them to make sure it fits their workflows.
Now, as far locking-in user data goes (as @adhg has mentioned), you should always provide the option of exporting all data uploaded by the user/customer. It's just good experience for them. An even better experience would be to allow users export their data after the trial ends if they decide not to convert to paying customers after all.