In this case the only thing one can do is send it by themselves. These things do happen with the kind of service we are talking about so either you will have to be patient despite their changing timelines or manage your application by self. I don't really see an alternative for you - you are in a tight spot.
The standard answer most people give in such situations is - you should have started early. I can understand your trouble but don't know what else to suggest realistically. Good luck and hope you receive soon!
PS - FBI changes timelines AFTER one submits due to the change in their pipeline, similarly WES changes response timelines at busy times. In fact I lost 1 - 2 days last year from WES because those guys put my case on hold although after I called they immediately moved things. And I lost my NOC last year by a day, so in effect because of the WES delay I lost FSW 2013. Sh1t happens!! The key is one has to start way in advance else there are always risks that bottlenecks might delay things.