Your RD is rather unfortunate because you're not eligible for fax inquiry until 7/16. The problem is that CSC had no JIT on 6/1 and you have to wait at least 30 days after JIT was issued with date that passed yours. The 6/16 JIT says 4/2, so you'll be eligible on 7/16.
What I'd do however is fax an inquiry on Monday saying your case has been pending for more than 60 days and JIT says 4/2 although you're 3/25.
Then wait 15 business days and e-mail an inquiry to div 12, saying that you're eligible for immediate adjudication because your case satisfies all requirements:
a) your case has been pending for well over 60 days
b) JIT on 6/16 said 4/2 and it's been over 30 days since (assuming 7/16 has passed)
c) you sent a fax inquiry to div 1 and got no response (you won't get it, be sure of that).
I did a similar thing and the case got RFE 3 days after e-mail.
If you don't know how to do a fax inquiry, look at BCIS CSC 2003 guidelines, there shoud be a link somewhere in the Forum.
Good luck.
And don't buy your plane ticket before you have your AP.
Also in no way leave USA without AP, never.