I completely hear you on your career being crazy important, and not wanting to do anything that may derail your plan. I just can't imagine anyone is going to really care, though (from that perspective). You know how you have a plan for your career? I can almost guarantee they have a plan for themselves, too. This means they are making moves to execute their needs, and have absolutely zero s**ts to give about anyone else. In this circumstance, this is a good thing!
Yes, if you are bony and lanky people may stare and/or comment (particularly if you're female). Who cares? I say this as a tall, lean women. Decide you have zero s**ts to give about what strangers have to say about your body, and just concentrate on your career. It's all good.
I would just be patient with people, and explain all this in as few words as possible. Say you have bite issues, or pain issues, or jaw issues, or something like that. Most people are good, and will do what they can to help.
The event you have at the 2 week mark, with employers, may be pushing it a bit...particularly, if it's loud and you're attempting to talk amongst/over others.
Cheers!