The first thing you need to do is find out whether an L-visa can be converted to a Z-visa in Henan province. Some provinces can do this, some can't. I know that for instance in Hubei province it can't be done. Some schools will ask you to go to Hong Kong to get the Z-visa, this is a hassle and the schools will not pay you for this, all the expense is on you.

You local Chinese consulate should be able to easily provide this information. If an L can't be converted to a Z in Henan then you should not work at that school. It will mean the school is lying and it also will mean that they very likely do not have a licence to hire foreign teachers. The school must be able to change your L visa to a Z quickly in Henan without you having to go to HK.

Many training centres illegally employ FT's, you need to be careful!