Can I renew/exchange my "L" Visa?!

My name is Basem, I am an Egyptian. I first applied to a M type with all the required documents stated on the website. It required a previous visit to china and I had that as a tourist. This time I applied for a "F" type but also got a "L" type with a single entry and maximum 30 days/stay.

I am now in China, doing an internship, and mine will expire in 1 week. I went to the police station to apply for an extension and the officer simply said, you are a tourist you can not extend it with out a travel agency. Which was not mentioned in any of the websites/forums I visited, NOR was it mentioned in the government website. Anyways this is the situation I am in right now and I would really like answers to some questions.

1. Can I extend my L type with out a travel agency or not?
2. Can I exchange my L type to a F type?
3. Can I do either of those with in china?
4. Whats the possibility of going to HK and applying to mainland China from there?

IF anyone has any other suggestion or idea, please let me know. I am desperate for an answer, otherwise I am forced to leave with out finishing what I came here to do.

For anyone wondering why I am in this situation...that would be because my travel agency in Egypt decided to not get back to me when the embassy said there are papers missing (even though i checked every item on the list) and they did that with out consulting with me.

Thank you in advance, please answer ASAP!