There's a legal answer and a practical answer. (This ain't legal advice, as I have no idea what it is that your app does).
In general, your legal tools as a business owner are relatively limited. The first is an NDA, which you know, and the second is making damn sure that every potential piece of IP resides in you and not in those you have hired to execute your idea. This is important for both patent and copyright (which can only be transferred in writing). You can supplement those tools with technologies that log developer activity and so forth (who emailed whom, what files were accessed, what was done when, etc.) in the event that you have to go to the mattresses. If you have to actually enforce those agreements, odds are you've already lost.
What I'm concerned about is that you sound like you may have a developer team that you don't trust entirely (?). That's a hard situation to be in.
There are two approaches where you are. The first is release, take advantage of the first mover effect, and run like hell. Promote your idea and upgrade on the fly. Give buzz for it so that people are excited. Other people will copy the concept for sure, and then it's on you just to execute better. As they execute, take a look at their patents. If there's no protection, don't be afraid to add additional features.
The other way is just to wait till it's nearly exactly what you envision. The dangers of perfectionism are obvious; it's not just delay, but also that organizations sometimes will not like to hear that the app is just not delivering what people want. It makes it difficult to change features that were months/years in the making. That is simply human nature. (Sounds dumb, but it happens all the time and is more likely in small environments).
I'm a believer in the first approach.