You'll only know for sure if you give it a go to try to get a 30 days' L visa. The only thing that they would definitely do is check if your name is on their centrally-maintained computer file of blacklisted foreigners, that is those who they never want to let enter China ever or again.
Your name wouldn't be on that file for having been issued a * visa or a 10-day exit visa,resulting only from relatively minor visa violations at worst on your part.
More importantly for you,it'll not be easy to get a teaching job on an F visa at this time as it's well into the first semester.So why bother trying to enter China at this time on a short L, your sole option in HK in any case?