You are correct that those who enter on a C-1 transit visa (not as a crewmen) are eligible to adjust status through marriage to a U.S. citizen although you will most likely have to explain your intent upon entry to the immigration officer. I just had a case like this and it was eventually approved but I had to educate the officer on the law because he thought my client was ineligible to adjust on a C-1 visa, no matter the circumstances of his entry. For a case like this, you should hire an experienced immigration attorney.
I agree with my colleague, C-1 is some instances are eligible for Adjustment of Status. However you need to be much more careful with this type of case, as there are a number of potential issues. For example you mention that you are aware of the jumping ship provision. If your visa was a combo C1-D1 visa you could face a stiff uphill battle. Here is a recent case denying eligibility to a C-1/D-1 that was admitted as C-1.
Though it likely goes without saying, marriage for the sole purpose of obtaining a Green Card is a crime, and immigration will hold you to a very high standard in establishing that your current marriage is in fact for the purpose of sharing your life with your US spouse, and not merely the limited purpose of a Green Card.
Even if you were simply out of status, I would strongly recommend using an immigration attorney. That you entered on a C-1 only strengthens this opinion.
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No. Entering with a C-1 means you cannot change you status in the US. You must process abroad.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.
This is one of those questions that even experienced immigration attorneys miss. In general, C-1 visa holders cannot adjust or change status, however there are exceptions. One exception is for a person who can avail himself of the benefits of 245(i). Consult an experienced immigration attorney; better still, two experienced immigration attorneys. Good luck.