Without a release letter, your new school almost certainly won't be able to get a foreign experts certificate for you. If you ask your present employer as to the possibility of leaving / paying breach penalties / release letters etc, your relationship will almost certainly sink to toilet levels, and you could be in a very bad situation; unable to leave an employer who doesn't trust you.
It's difficult to offer advice when I don't really know all the ins and outs of your situation, but these are the assumptions I've jumped to.
You don't really know your new employer yet.
You can't possibly know whether your potential new employer is a good one.
You're in a new city so you don't possess enough local information and knowledge to make a good decision yet.
You're working at a University, but it sounds as though the new job would be at a language mill. The thing about Unis isn't the 'pay rate', it's the small number of hours meaning that you have more freedom and wiggle room, including acquiring part-time work at anything from 150-300 per hour.
I don't doubt that your new job is sucky, but a year on the ground will allow you to make a more informed decision.
If your leaving would leave your current employer in the lurch, I'd expect them to be very annoyed, and they absolutely could make your life a living hell.
Why on Earth would a new school be prepared to pay the breach penalty?
Anyway, unless you know for certain that your current employer are going to be amenable to you leaving early (because for instance you have first hand knowledge of someone else that they've let go early and have given a release letter to) then making any kind of move would be remarkably dangerous.
People should only 'break' their contract if they're in a terrible position (and even then there's a strong argument for staying) or when it's obvious on both sides that a mistake has been made and a divorce is the best option for everybody concerned. This does happen. Schools sometimes realise that they've made a big mistake, and they're only too glad to give a release letter to get rid of their recently acquired looneytunes.
So, it may be worth trying to find out how your employer feels about you by asking if they're happy, while pretending at the moment that you're delighted to be there, and only want to ensure that they reciprocate your feelings of adoration for them.
I think that some new saloonies have probably made rash decisions regarding their choice of employer, and I can only reiterate that contracts in China are often not easy to get out of, unless you're prepared to leave China altogether.