Can I apply for an H1-B visa while I am waiting for the change of status to H4?


Here is my case:

I have applied for J1 waiver in Feb. 2017.I have received my J-1 waiver in 25th July. My wife has applied for her H1B in 28th July.My J1 visa expired on 31st July. I have 30 days of grace period (until 30th Aug. 2017) My wife received her H1-B in 15th Aug.I submitted for the change status from J1 to H4 on 17th Aug.I received the application receipt on 28th Aug. (two days before the end of grace period!) So I don’t need to leave USA.I have to travel to Canada on Oct. 15th! Because the H4 application could possibly take several months to process. I am wondering whether I can ask my future employer (a university in the usa) to apply for the H1B visa for me in this September? Or in other words,

whether can my future employer could file the H1-B petition while I am still waiting for the change of status to H4?

If this is case, I might need to withdraw my application for H4, am I right? If this is doable, then with the premium processing service, I will be able to obtain my visa in this month, which will enable me to travel outside of the US in Oct.

Thank you very much for your great help!