The only thing is that this is not a free service, so I want just a couple users to flesh things out and get some new opinions, before releasing something that flops and gets a bad rap.
You seriously don't have to worry. And if your service is so amazing and wonderful that people are frantically sharing your signup then you have a very good problem to deal with.
Even then you can shut it down in an instant and even (shock, horror) email the people who you don't know and tell them you're really sorry but you're disabling their account because it's a private beta. And you'll let them know as soon as it's live. And they can get immediate access then.
Because if you're sending out invites you know who you sent them out to right?
As for it being a paid service, make it clear on the signup page it's free now but you'll be charging for it as soon as you're out of beta. No-one;s going to complain. Give a rough price if you feel like it, but make it clear it's rough. You're making a mountain out of a molehill here.