It is too bad that the inmate did not know about making a PC 1381 demand with regard to the misdemeanor. With regard to his release date, if his prison sentence is complete, then he is being held pursuant to the warrant. One way to find out how long he may be in custody before being transported is to call a bail bondsman in LA county. Also, you should check the amount of the bail for the misdemeanor warrant.
Ask the inmate whether they filed the 1381 demand and if so, if they have any paperwork indicating they did. I have often had clients indicate they filed the demand but nothing happened and then they had to deal with it once they were released from prison custody. I don't know how long they can continue to hold him past his release date but it seems that if San Diego is not going to release him unless LA picks him up, but they are telling him that LA isn't going to pick them up, well then they would be holding him illegally.
If i were handling the case I would probably call the court that the case is out of and ask them for a removal order for the warrant. That might expedite things.