Are you a cost reimbursable contractor or a government employee? I am surprised they allotted you a maximum dollar amount to airfare on a business trip. Even if they do that, you are typically not permitted to fly in J.
Either way, you might have to get an exception to the act. It is pretty painless...there is a simple form to fill out depending on your organization. See some rules below. Contact your travel/contracting department.
For travel outside the U.S., if a U.S. flag air carrier provides service between your origin and
destination, you must always use a US flag carrier for such travel unless, when compared to using a
foreign air carrier, such use would:
1. Increase the number of aircraft changes you must make en route by 2 or more; or
2. Extend your travel time by 6 hours or more; or
3. Require a connecting time of 4 hours or more at an overseas interchange point.