Changing from L visa to X2 type within China

Hello!

I am a EU citizen, but studying full time in Hong Kong, therefore also a HK resident card holder. I will be studying in Tsinghua for one semester, starting from February, but I need to enter China already on 4 January to do a short, unpaid internship in Beijing, which would most likely not qualify under the business type.

There would be no problem if I could apply directly for X2, but in order to do that, one needs the admission documents from the local university. Tsinghua issues these only in January, therefore I have to enter China with another type.

What do you think is the best option for me? Apply for a 30-day L type and then apply for X2 within China? Would that mean I'd have to come to HK to activate the student type? I also found that there exists an F type (for cultural exchanges, visits and study tours in China) - does this one have any limitations in regards to its length and would that be possible to apply if I submit an invitation from my entity?

Thanks a lot