If this is a concern (which it should not be to be quite frank), you could have people lock their apps on their journals and grant access to the mod journal after posting. If they are rejected, then only the mods need to know why.

But this is fallible too, because now players are robbed of the chance to know what a quality app was. Was the app for Bob from Popular Canon not as good as Larry from Obscure Canon? Was Bob accepted at Larry's expense so someone 'cool' could get in?

There's no perfect solution to app capping. But I think the smallest sacrifice comes in having apps open, where everyone can see them, and so the process of fairly processing them is seen by all.