B747-200 FLC ENCOUNTERS WX AND DEVIATES OFF ASSIGNED COURSE.

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SOLID LINE OF TSTMS 30 DEGS PERPENDICULAR TO OUR TRACK. RADAR INDICATED BEST DEV TO THE L OF TRACK. CONTACTED RADIO ON HF; REQUESTED '20 MI DEV TO L OFF COURSE DUE TO CUMULUNIMBUS.' AT THAT POINT WE WERE APPROX 110 NM E OF LINE. PURSER WAS ADVISED THAT CODE 4 PROCS WOULD BEGIN IN 10 MINS; LASTING UP TO 20 MINS. PURSER ADVISED ME WHEN CABIN WAS PREPARED. ADDITIONAL PA TO PAX MADE FROM FLT DECK. 6 MINS AFTER REQUEST; RADIO ADVISED THAT ATC DENIED OUR REQUEST FOR WX DEV. AT THAT POINT; DEV TO THE R WAS IMPOSSIBLE BECAUSE OF PROX OF WX AND TURN RADIUS AT OUR TAS. I ASKED THE FO TO CONCENTRATE ON ACFT CTL AND TO FOLLOW HEADINGS I ISSUED TO DEVIATE CELLS. IGNITERS AND ENG ANTI-ICE WERE ON. I ASKED THE SO TO MAKE ADDITIONAL PA REINFORCING THE NEED FOR PAX TO REMAIN SEATED. WE DEVIATED L OFF COURSE APPROX 12 MI TO AVOID LEVEL 5 TSTMS WITH TOPS ABOVE FL400. WE WERE UNABLE TO CONTACT RADIO WHILE IMC DUE TO P-STATIC ASSOCIATED WITH THE TSTMS. APPROPRIATE WX DEV PROCS (NO RADIO COMS) WERE INSTITUTED (AIR TFC CTL P-10). NOTIFICATION TO OTHER ACFT WAS MADE ON 121.5 AND 123.45. ACFT LIGHT ON; TCASII ON. WHEN DEV EXCEEDED 10 NM WE DSNDED TO FL347. WHEN DEV WAS COMPLETED; WE RETURNED TO FL350 WHEN WITHIN 10 MI OF TRACK. MAX TURB EXPERIENCED WAS MODERATE.