I just got back from my info-Pass Appointment (87th day from the receipt date). To my surprize, the officer I met was very kind, he looked into my case and told me that someone had recently started working on my case on the 18th June. He also put in a request to speed up since my travel on July 2nd was fast approaching. He told me to come back if I did not recieve my AP in the next 7 days in which case he will issue me an AP there itself!
At least now I have the assurance that I will be able to travel after all! I strongly recommend anyone going through a similar situation to do that.
FYI, my online case status still shows "initial review"
Good Luck everyone and thank you for all your responses!