X1 Visa -- Exit and Re-enter?

Hi all,

I have an X1 student type with multiple (多) entries. I entered China on September 5, so thirty days from then would be October 4. However, because of various issues, I haven't been able to do an in-country physical exam until today. Because of Golden Week next week (Oct 1-7), I can't pick up my health certificate until the 8th which I need to get the Temporary Residende form and apply for the residence permit.

Do you know how much the fine would be for overstaying?

Alternatively, do you think I could exit mainland before October 4 (maybe go to Hong Kong or Taiwan) and re-enter to reset the 30 days?