Yes you can
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Yes you can. The five years of L will count towards the six years of H1B max time. On occaision, CIS has denied such applications claiming that your year out of the country must be completed at the time you file the application (4/1/2013) rather than the employment start date(10/1/2013). In your case, because you only have the five yeasr towards the max, you could still file it. In the most conservative manner, you could file for the one year as an H1B and then either extend the approval or file an amended petition to show you are eligible for a new six years.
I don't know your situation, but I'm surprised that your employer did not change you to an H1B effective 10/1/2012 or start a green card process for you.