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3 Answers
Tim Graham
I would look into academic / non-profit opportunities. Usually they are more lax about the 4 year thing than a mega-pharma company would be.
Sherri Homanko
Have you considered contacting a head hunter?
http://money.usnews.com/money/blogs/outside-voices-careers/2015/03/24/5-tips-for-recruiting-a-headhunter
http://www.headhunter.com/
http://www.forbes.com/sites/deborahljacobs/2012/07/26/7-things-a-headhunter-wont-tell-you/#367aad0c10c7
Maybe the links above will help you with your goals.
Sherri Homanko
Have you tried applying with any agencies? Some of the agencies may be able to lead you into a temporary job in your field that can lead to a full time job.