can I extend my visa in China if I am on an L visa after having overstayed within the past 6 months?

I overstayed in China a month ago and I was given a 10 day star visa.
I went to HK, where they gave me a one month L visa which is about to expire now. I was planning to extend it for a month now and then go back to Europe or Hong Kong to get a 6 months F visa.
I just read now on a website that I cannot apply for a business visa in HK if I have an overstay record.
I don't know if this is possible in Italy (where I am from)
Now I'm also starting to worry that they might not extend my L visa for the coming month.

Anyone knows anything about this? (before I panic)

Thanks!
g