Route 1:
J1 has grace period and you can get H1 in 2 weeks with J waiver. You might not need to leave, even if you do, the time out side USA will be very short.
Route 2 is not suggested for you, because N400 takes longer than 1 year in some places so you won't be able to work for maybe two/three years before you get EAD.
In your case, you are not desperate, you have a job offer (that you will only get hired in legal status)
J1 has grace period and you can get H1 in 2 weeks with J waiver. You might not need to leave, even if you do, the time out side USA will be very short.
Route 2 is not suggested for you, because N400 takes longer than 1 year in some places so you won't be able to work for maybe two/three years before you get EAD.
In your case, you are not desperate, you have a job offer (that you will only get hired in legal status)