NON ADHERENCE TO ATC CLRNC BY ACR FLC AS THEY ATTEMPT TO AVOID TSTM ACTIVITY BY CREATING A HDG TRACK DEV.

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THE FLT WAS IN CRUISE AT FL310 APCHING THE ZUNI VOR FROM THE E. WX WAS HIGH CIRRUS WITH BUILDING CUMULONIMBUS 5000-10000 FT ABOVE OUR FLT LEVEL. THE CTR CTLR HAD ASSIGNED US A 230 DEG HDG TO INTERCEPT THE ZUNI 242 DEG RADIAL W OF ZUNI ON THE FOSSL 3 ARR TO PHOENIX. THE CTLR AND THE RADIO FREQ WERE EXTREMELY BUSY THROUGHOUT THIS ENTIRE PERIOD. THE 230 DEG ASSIGNED HDG WAS TAKING US INTO THE CTR OF A LEVEL 2 TSTM WITH TOPS ABOVE FL390. WE ATTEMPTED TO CALL THE CTLR TO INFORM HIM WE NEEDED TO DEVIATE TO A 215-220 DEG HDG FOR THE TSTM BUT COULD NOT GET THROUGH BECAUSE OF THE VOLUME OF RADIO XMISSION. WE WAITED AS LONG AS WE COULD AND THEN TURNED TO A 220 DEG HDG FOR SAFETY REASONS. WE HAD JUST ROLLED OUT ON THE 220 DEG HDG WHEN THE CTLR ASKED US OUR HDG. WE IMMEDIATELY INFORMED HIM AND HE GAVE US AN IMMEDIATE DSCNT TO FL280 AND RETURN TO THE 230 DEG HDG. THIS WAS TO DECONFLICT WITH EBOUND TFC AT FL310. WE COMMENCED A DSCNT AT 2000- 3000 FPM AND TURNED BACK TO 230 DEG HDG INTO THE SOUTHERN EDGE OF THE CUMULONIMBUS. WE HAD THE CONFLICTING TFC IN SIGHT THROUGHOUT; AND THE OTHER ACFT RPTED US IN SIGHT. THE ESTIMATED PASSING DISTANCE WAS 1500-2000 FT VERTLY AND 4-5 MI HORIZ. THROUGHOUT THIS MANEUVER WE DID NOT RECEIVE EITHER A RESOLUTION OR AN ALERT ON THE TCASII. THE CTR CTLR DID NOT INFORM US WHETHER HIS ALERT SOUNDED OR NOT. FACTORS INVOLVED: EXTENSIVE TFC AND RADIO SATURATION. EXTENSIVE TSTMS IN THE AREA AND EBOUND TFC AT INCORRECT FLT LEVEL.