Under the NLRA, you cannot be required to be a member of a union or pay it any monies as a condition of employment unless the collective bargaining agreement between your employer and your union contains a provision requiring all employees to either join the union or pay union fees. Because you are in a closed shop, the agreement would prevent you from holding the job if you failed to pay dues. If the job allowed non-union members, then you could not pay dues and still receive protection. But again, in a closed shop, this is not the case.
That being said, in these types of union agreements, they usually have very strict guidelines setting forth being hired in a position, being fired from that position, and the process in which this may happen. Usually speaking, you cannot be forced to work in another classification at a reduced pay. This would be considered constructive termination. You would want to contact your union steward and explain what has happened. In the event that they fail to do anything you can file a formal complaint with the NLRB. This can be done here:
However, to actually have a claim, there must be some provision in the union contract which discusses this. Absent this, California is an at will employment state. This means that the employer can change the conditions of your employment for any reason they see fit, at any time. This is ultimately because they are technically firing you, and rehiring you at the different position. If this is the situation, then the only remaining option would be to file for unemployment and claim, quite rightly, that you were constructively terminated, (i.e. the terms of your employment were materially changed). In this instance, the unemployment department would grant you benefits as long as you met all of the other requirements (e.g. amounts paid in, etc.)
But again, the union contract likely prohibits the changing of duties and rates. As for "re-clocking" you must be paid for "all hours worked." So, if they are asking you to clock hours less than what you worked, then you likely have a legitimate overtime claim, especially given the change of duties they mention. More about that can be found here:
If that is the case, and the union fails to help you, then you also may want to consider getting an employment attorney involved. If you decide to hire an attorney a great resource is www.Martindale.com. This is a nationwide directory that is useful in finding highly qualified legal specialists in various fields of law. The lawyers in Martindale are not selected because they paid to be included, but rather because they have been rated by other attorneys as qualified experts in their field. Consider consulting with two or three different attorneys willing to take your case prior to selecting the one you feel most comfortable with. In a case like that, an attorney would take your case on contingency, which means that you would end up paying nothing out of pocket.
If you have any other questions or need additional clarification, please do not hesitate to ask.