A B737-300 FLT CREW RPTS SOCAL APCH CHANGED RWY AND TRANSITION CLRNC AFTER PASSING CIVET ON THE MITTS ARR TO LAX. TRACK DEV AND VECTOR TO PREVENT LOSS OF SEPARATION.

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ON INITIAL RADAR CONTACT WITH SOCAL (HEC TRANSITION); CLRED TO DSND VIA THE MITTS TWO FOR RWY 24R PRIOR TO CIVET RWY CHANGED TO RWY 25L. FMC REPROGRAMMED FOR RWY 25L. OVERHEAD CIVET WITH ACFT TRACKING TO BREMR FOR RWY 25L; SOCAL RECLRED US FOR RWY 24R. CAPT NOTIFIED ME OF RWY CHANGE AND LOADED WAYPOINT ASUYA AND RWY 24R. I BEGAN A GENTLE TURN TO APPROX 330 DEGS TO RESUME/INTERCEPT THE ARR TO RWY 24R (THE FMC WAS INDICATING A TURN TO THE N -- 360 DEGS TO ASUYA -- WHICH SEEMED TOO EXCESSIVE). AS WE WERE DISCUSSING THIS NAVIGATION SIT; SOCAL QUERIED US TO WHERE WERE HEADING AND ASSIGNED US A VECTOR OF APPROX 260 DEGS TO INTERCEPT THE RWY 24R LOC. TFC FOR THE S COMPLEX (RWY 25L) WAS HELD UP UNTIL WE CROSSED BELOW THEM. REMAINDER OF APCH/LNDG TO RWY 24R UNEVENTFUL. CONFUSION FOR THE ARR I BELIEVE BEGAN WHEN SOCAL RECLRED US FOR RWY 24R (THE PREFERENTIAL RWY FOR COMPANY) AT CIVET. IN HINDSIGHT; SOCAL WAS PROBABLY EXPECTING US TO TRACK CIVET CAMOM ASUYA. WE WERE NEAR/OVERHEAD CIVET AT THE TIME OF OUR NEW APCH CLRNC; OUR FMC HAD LEAD-TURNED CIVET AND WAS TRACKING TOWARDS BREMR FOR RWY 25L. SINCE AT THIS POINT WE HAD NO FMC SOLUTION TO TRANSITION TO RWY 24R I BEGAN A TURN N OF OUR CURRENT TRACK WHILE THE CAPT REPROGRAMMED THE FMC FOR ASUYA TO TRACK FOR RWY 24R. THIS LAST MINUTE RWY CHANGE AT CIVET WHERE THE ARR BRANCHES OFF ON THREE DIFFERENT TRACKS (RWY 24/RWY 25R/RWY 25L) LED TO THE CONFUSION ON THE APCH BETWEEN US AND ATC AND LED TO THE NAVIGATIONAL DISCREPANCY AS OUR NAVIGATIONAL COMPUTER HAD ALREADY BEGUN TRACKING FOR BREMR FOR RWY. WHILE A RWY CHANGE TO RWY 24 IS MUCH APPRECIATED; THIS LATE ON THE ARR; A VECTOR TO INTERCEPT THE RWY 24R LOC WOULD HAVE BEEN MORE HELPFUL (AND IS WHAT WE EVENTUALLY RECEIVED FROM SOCAL). SUPPLEMENTAL INFO FROM ACN 678218: THE RADIOS AT THIS TIME WERE COMPLETELY GARBAGED UP WITH PEOPLE STEPPING ON TOP OF EACH OTHER; SOCAL STRESSING OUT; AND EVERYBODY GETTING FRUSTRATED. JUDGING BY THE TONE; FRUSTRATION; AND SPEED AT WHICH THE CTLR TALKED; IT WAS APPARENT THAT THEY BLAMED US FOR NOT COMPLYING WITH THEIR INSTRUCTIONS; WHILE THEY FAILED TO REALIZE THE ILLEGAL CLRNC THEY GAVE US. ADD TO THIS THE HUGE DISTRACTIONS OF NUMEROUS FREQ CHANGES; AND THE EVER INCREASING RADIO CHATTER ON SOCAL'S FREQ; AND IT'S NOT HARD TO SEE HOW THINGS CAN GET MESSED UP VERY QUICKLY. ALL I ASK IS THAT THEY DO ONE OF TWO THINGS; EITHER GIVE US A HDG TO FLY OR DIRECT TO A FIX ON THE OTHER TRANSITION.