A320 FLC WILL NOT FLY INTO LINE OF THUNDERSTORMS AND IS TOLD TO SQUAWK 7700.

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FLT FLL-DTW; HEADING 330 TO REMAIN W OF TWO AREAS OF TRWS WITH ASSOCIATED VISIBLE MERGED BLOW OFF. THESE AREAS WERE ORIENTED ON E/W LINE DISRUPTING N/S FLORIDA TFC FLOW. WERE LATER CLRED TO FL370 WITH ANTICIPATION OF TURN ON COURSE ONCE CLBING ABOVE LINE. IN TURN ON COURSE; INSTRUCTED TO RETURN TO FL330 WITH EASTERLY DEVIATION AND ADVISE NEXT CTLR (134.57) OF WX DEVIATION REQUIREMENT. ON FREQ CHANGE CHK IN; ASSIGNED HEADING OF 080 FOR TFC. I ADVISED UNABLE DUE TO WX. ATC RESPONDED WITH SQUAWK 7700 AND SAY INTENTIONS. I RESTATED; UNABLE TO TURN INTO TRW BLOW OFF AREA. HE RESPONDED WITH; 'SINCE YOU'RE UNABLE TO COMPLY WITH ATC INSTRUCTIONS; SQUAWK 7700 AND SAY INTENTIONS.' ATC TURNED OTHER TFC AND SUBSEQUENT COM WITH THAT FLT DELAYED OUR RESPONSE. A LESS OMINOUS AREA PRESENTED ITSELF ALLOWING OUR ACCEPTANCE OF 070 ASSIGNED HEADING. I DID NOT DECLARE AN EMER. WE PENETRATED 'WEAK' BLOW OFF AREA ENCOUNTERING CONTINUOUS LIGHT TURB WITH OCCASIONAL MODERATE BUMPS. SUSPECT WE WERE HANDED OFF TO AN ALREADY SATURATED CTLR AS A CONFLICT WITHOUT ADEQUATE TIME FOR RESOLUTION. THIS IS THE FIRST TIME I'VE HAD A CTLR DEMAND I DECLARE AN EMER. NEXT TIME; I PROBABLY WILL. THE END RESULT WOULDN'T HAVE CHANGED AND MAYBE IT WOULD HAVE IMPROVED COM. SUPPLEMENTARY INFO FROM ACN 543117: HAVING COMMITTED WITH THE PREVIOUS CTLR TO GO W AROUND WX AND CLB; A MAJOR CHANGE IN HEADING TO DUE E WAS REQUIRED TO AVOID ENTERING RAPIDLY BUILDING; MERGING LARGE CELL LINE. CAPT REQUESTED CLB OR DSCNT TO ACCOMMODATE MIA CENTER; WHEN UPON CHECK IN ON FREQ; HE NEEDED A TURN TO THE N; NOW. THE CAPT REPLIED UNABLE TO ENTER LINE OF STORMS WITH A NORTHERLY HEADING. AFTER A SLIGHT PAUSE WHILE THE CAPT AND I DISCUSSED PLAN OF ACTION. CAPT EXPLAINED HE WOULD BE FLYING US DIRECTLY INTO BLOW OFF AND TRW (RED ON SCOPE) LINE TO WHICH CTLR AGAIN REPLIED SQUAWK 7700 OR TURN TO HIS ASSIGNED HEADING. RELUCTANTLY WE COMMENCED A TURN INTO THE BLOW OFF (IMC) ANVIL AND THE CAPT INFORMED HIM WE WERE TURNING NORTHBOUND. WE WERE UNCOMFORTABLE WITH THIS ATC STEER WHICH WAS DIRECTLY TOWARD 3 LARGE RED BUILD-UPS OF TRWS ON OUR SCOPE. RATHER THAN FLY DIRECTLY INTO THE CELLS THE CAPT INFORMED ATC WE COULD PROCEED DIRECT CRG VOR AND AVOID THE BUILD UPS. ATC REPLIED 'UNABLE' AND GAVE US A STEER OF 330 DEG WHICH DID BARELY CLR US OF THE WX BUILD UP WE WANTED TO AVOID. A SWITCH TO THE NEXT CTLR (JAX CENTER) RESULTED IN A TURN ON COURSE AND CLB TO 370. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: PIC WAS VERY CONCERNED WITH CTLRS INTENT OF PHRASE 'DISREGARDING ATC INSTR.' THIS CAUSED ADDITION WORKLOAD FOR THE FLT CREW. THEY ADVISED THEY WERE NOT GOING TO FLY INTO A LEVEL THREE RADAR DISPLAYED WX SYS; BUT COULDN'T UNDERSTAND WHY ZMA WOULD NOT PROVIDE THEM ANY ALTERNATIVES; ESPECIALLY WHEN TRANSFERRED TO ZJX THEY WERE ISSUED AN ON-COURSE RTE AND CLB CLRNC.