A few facts about my case:
1) the illegal work occurred in 2008-2009, then again in 2012-2013. The new job will start
August 2014

August 2014? What's giong on? This is 2015!

I plan to explain the situation to my employer, and write a different resume that does not
list my China employment for them to submit with my employment license application.

You'd better not explain the situation to your employer. Write a different resume to disguise your illegal employment. Since you have a new passport, it will be impossible for your prospective employer to identify your illegal employment, but don't disguise the facts. You vacationed in China during those two periods when you had gotten tourist visas for China.
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