I have about the same problem...
My J1 expires June 30th and school starts on aug 27th.
I wanna get my visa here in the US,so my question is,
what I can do for those two months in between.
If I sent out all my stuff for the status change and didnt get accepted till after june 30,
would that be ok then to be out of status?
And what if I get before my expiration date?
Do I need to get a visitor visa?
Thanks for your help!