Make a signup page to be part of the beta, include the disclaimer that it's free during the beta but once the service is publicly available it will be charged f

Make a signup page to be part of the beta, include the disclaimer that it's free during the beta but once the service is publicly available it will be charged for and the fees are waived during the beta in exchange for bug reports, possible issues/downtime, etc. Then, whenever someone signs up, just automatically send them an invite. You don't limit the people who want to use it in the beta and can provide valuable feedback and you set expectations appropriately for leaving free status and to the state of the application. And if you think that you may get a bad rap for being in "beta" and it not being as good as Google's beta, just call it "alpha" instead.