J2 visa holder apply a new J1 visa before entering the US

[Fuyu]

I just obtained the J2 visa this week. And, today I was interviewed by a university from the US. The tricky situation is that the potatial new boss prefers a starting date ealier than the date when my husband (J1 visa holder) go to the US.

My question is that whether I can apply a new J1 visa with a J2 visa at hand. If I can, there will be two months for the new application.