Even though you have not signed the contract, visa is totally a different matter altogether. A Contract becomes important when you start working for the organization. From what I understand, your employers are playing it "dirty". They are keeping you in a limbo. The moment you sign a contract and it gets legalized, they will be in trouble if they don't get you under a visa and get you an QID.
As far as I can understand, in your case you can do just nothing. You can go for a new employer only after your current employer is willing to give you a NOC or cancel your visa.
My suggestion is that, you sign the contract and get it legalized. After that if the company fails to get you RP and a QID, they will be held responsible. Also, you should drop the idea of transferring to another company. This may not be possible in your circumstances.