Is it permissible to pay a person 30,000 Saudi Riyals in exchange for transferring me to a job in my father's city, given that official transfer methods have proven impossible?

If the transfer is indeed your right, and the man is not the responsible employee, and he will strive and utilize his connections to secure your right without deceit or fraud, then there is no harm in giving him a commission for his effort and work. Bribery is when money is taken to validate falsehood or invalidate truth. However, if a person is wronged and gives something to someone who intercedes for him with the ruler to achieve his deliverance and protection, then this is not unlawful bribery; rather, it is a permissible commission (ju'alah).