Sigh.
To all the people getting on their high horse with "run! run! run!" advice, bear in mind that the OP probably doesn't have a lot of other options here. It's not like he's already working and considering a move, it doesn't sound like he's well established in the international teaching system where he can choose from a range of countries around the world to work in, this sounds like his first job.
It sounds like the local system is just totally inflexible (is this a surprise to anyone in the slightest?), and HR isn't exactly known for thinking out of the box. Having a verbal explanation of benefits over the phone, having plenty of time to read a contract on site, having someone onhand to answer questions, should mitigate a lot of other concerns.
Given how messed up things are at the moment, having a job offer is probably better than not having a job offer.