Yeah, some products lend themselves to an obvious upgrade path (like my own where increased usage brings charges). When you find yourself in this situation it makes sense to offer a free tier as a gateway. We also get some (small) promotional value from our free users as well. But for your product it's not obvious that having free users will provide you with much value and if they don't transition to paid, then they are very much a dead weight.
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.
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.