Upvote:1
You can ask your employer for an H1B visa instead of a J1 visa.
More to the point, if you are currently working on contract on an ESTA then you may be in violation of American visa laws. You are not permitted to work on ESTA status and violating this can lead to you getting deported and banned from the USA. So before you do anything else, stop working and clarify your current status.
It sounds like you need to hire an immigration lawyer.