We are considering J because the boss doesn't want to spend too much money on H1B premium processing. Regular H1B is ok and she wants me to start early.
-Why don't you just pay the premium processing fee ($1225) by yourself to get the H1 status? Many people even pay the entire H1 petition fee to get the H1 status even if the law requires the employer to pay it. In US, sometimes you have to compromise for your maxium interests.