BTW: I think that this the sort of service where Freemium doesn't make sense. You need people to get value out of the system, not offer them some crippled version for free and hope they will upgrade.
With this sort of service it is best to offer everything with a generous trial period.
Once someone has their data in your system they will want to pay you when the time comes as they have invested their time to get their data into your system. But getting people to convert will depend on whether you are offering them true value, and this can be best achieved by exposing all the value from the start.
That said, having people as free users and then cutting them off without warning could have a negative PR effect.
I think the easiest course of action is to put some wording in a prominent place on the site to the effect of "this is a free beta, but we will be moving to a paid model when we feel we are providing enough value". Then when the time comes, it won't come as a surprise. Then you put them on the 30/60/X day free trial (which you have anyway for new paid users) and they can transition.
Sure, you will lose some of those free users along the way, but unless they are providing value to you, free users are just going to be a drain on your limited resources.