Premium process is better

You don't need to worry about the H1 quote. There is unlimilted for University researcher. The only thing you need to worry about is the processing time. Usually it need to take at least 3 month to get the H1 approved now. So premium process is better, it only need 15 days. You can try to let your boss do it. If he don't like it, you can tell him you like to pay this $1000. It is normal.

You need to know, your salary is much more than this $1000.