Congratulations on the launch of your Beta testing! That is half the battle. My advice would be to slowly do another round of Beta testing and inviting people who you know will give you good feedback and help you improve your app. Then in the mean time get PR to pump up your app again for launch in a month.

Not every app when it launches is perfect, we all have to update apps on our phone constantly so do not be afraid to go live. If you would like to set up a phone call I would love to chat more in depth because I have two friends who have get apps that I may be able to connect you with who have been in the same shoes as you!

In my experience advising start-ups, you can never get enough hand's on time with customers, or potential customers. As Steve Blank says, get out of the building. Too many time opportunities are missed because the founder waited until he/she felt everything was "perfect". Your level of perfection can only be truly judged by the customer.
One of the advantages of doing beta testing is that your users will understand that the product/app may not be flawless and certainly will not contain every feature that they would ultimately want. So put it out there and engage your users in meaningful conversations about their experience. Listen hard to try and understand two main things: if the user doesn't like something, why? If they do, why? It's just as important to understand the reasons for your success as it is your failures, because at the end of the day, you win or you learn.
Good luck, and feel free to contact me as you learn. I may not know your domain, but I know about listening to customers.

MVP, MVP..... Go as simple as possible, and make small changes often. Add feedback functions to keep the buzz, and include your clients in the process, they then get the pride of ownership... Think Pre-Launch, MVP0.1 Launch MVP1.0, timely revisions on feedback, build tightest customer engagement ever. I run a platform company that has nightly Revs on Apps, weekly revs on workflows, all customer driven.

Media and buzz are good, clients are better!

For the most part I would agree with the other commenters. We ran into this when we launched our app. We pushed to get our iOS out quickly to have it in user hands. That took resources away from our Android, which ended up taking several months to get out. In that time we lost a lot of momentum. So, in the world of a million apps, any buzz you can get is good and you need to capitalize on that. Users are fickle and you can easily lose them. However, make sure what you deliver really is what users want so you don't turn them off. It seems like you're already on the right path and as long as your current version provides value to the user, I don't see a reason to wait to get it perfect.

Fee free to reach out with any questions.