Account dropdown location

Is it possible to move the Account field dropdown? I would prefer this dropdown be all the way to the left rather than the middle of the screen. With EACH request being created, the Account is selected is key and I've had users create a ticket then realize the Account is wrong. So, when they change the Account all they've typed is cleared out. I believe you can change the Site which will change the Account but I would rather avoid this situation completely. If it means editing an underlying HTML page every time we do an update, so be it...we can add that into our updating process. I want to move the drop down to the left of the Incidents dropdown.

Thanks,
Mike