It sounds like you are going abroad and returning with a new SEVIS number/new I-20, so no gap in status. I don't think status would be the problem here - at worst, yopu could obtain the H-1B stamp abroad and reenter.
The problem is, it doesn't sound like you will graduate from your program until after the H-1B petition would be filed. If this is a Master's program and you plan to qualify based on your existing bachelor's degree, this may not be a problem - but if this is a Bachelor's program, you may not be eligible for the H-1b in time.
Seek the guidance of an attorney.
I have obtained H-1B visas for out of status F-1 students. A violation of F-1 status won't directly impact the H-1B petition, but if selected, you may need to depart the U.S. and return on the H-1B visa prior to the H-1B start date. Consult with an experienced immigration attorney to discuss the nuances of this situation.
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