B737 FLC QUESTIONED BY LAX FOR SLOW MOVEMENT WHILE EXITING RWY AS L29A LNDS.

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WE LANDED ON RWY 24R. THERE WAS A COMMUTER ACFT ON THE FORWARD HIGHSPEED TXWY Y AND A B737 ON THE REVERSE HIGHSPD TXWY Y. THERE WAS A B747 TAXIING INTO POS ON RWY 24L. I PLANNED ON ROLLING TO TXWY AA PASSED Z AND Y; BUT WAS SLOW ENOUGH TO EXIT ON Z OR Y. TWR TOLD ME TO TAKE THE 'FORWARD HIGHSPEED' EXIT. I SLOWED AND EXITED THERE. UPON EXITING; TWR TOLD ME TO TAKE THE 'REVERSE HIGHSPEED' TXWY. I MADE A VERY SLOW SPD SHARP TURN TO TXWY 'Y'. IN THE TURN I SAW A CORPORATE JET ON A VERY SHORT FINAL FOR 24R. I WAS OFF THE RWY PROPER (OUTSIDE THE WHITE LINE) BUT WAS NOT ACROSS THE YELLOW LINE ON TXWY 'Y' BEFORE THE CORPORATE JET LANDED. THERE WAS NO DANGER TO US OR THE LNDG ACFT; BUT WE WERE NOT COMPLETELY OVER THE YELLOW LINE WHEN THE OTHER ACFT TOUCHED DOWN. LAX TWR ASKED ME TO CALL HIM; AND ASKED ME WHAT HAPPENED; AND WAS I OFF THE RWY WHEN THE CORPORATE JET TOUCHED DOWN. SUPPLEMENTAL INFO FROM ACN 519974: LANDED 24R LAX; EXITED TXWY (Z) BEHIND A BRASILIA COMMUTER. AS WE CLRED RWY 24R TWR CTLR ASKED US TO USE THE REVERSE HIGHSPEED (TXWY) YANKEE. A 737 WAS HOLDING SHORT OF 24L ON THE SAME TXWY (Y). AS THE CAPT COMPLIED WITH ATC; I NOTICED A JETSTAR ON SHORT FINAL FOR 24R. THE CAPT IMMEDIATELY EXPEDITED HIS TAXI. OUR ACFT APPEARED WELL CLR OF ALL ACTIVE RWYS AT THE TIME OF TOUCHDOWN OF THE JETSTAR ON 24R.