I know you will lost a lot in this offer, but you have to accept the fact that it is really impossible to transfer.
even if you cancel your current visa and exit the country and return for a new visa still you can unable to get the job without NOC from the company.

and believe me even if you have a chance to get NOC you still have 50/50 chance to get visa under QP. immigration dept have the right to reject expat visa for QP when they can give to Qatari (the position) instead. and QP have no control over this.