PLT OF AN SMA SEL ACFT DEVIATED FROM ASSIGNED ALT DUE TO LACK OF ACFT CTL IN TSTM WX CONDITIONS.

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WERE APCHING MTH FROM CRE. AT THIS POINT; OUR IFR CLRNC WAS 'DIRECT MTH' AT 8000 FT MSL; AND HDG 190 DEGS. OUR WX STORM SCOPE WAS INDICATING THE PRESENCE OF CONVECTIVE ACTIVITY IN THE AREA OF THE ARPT; THE EXACT LOCATION OF WHICH WAS DIFFICULT TO DETERMINE; BUT IT APPEARED TO BE TO THE N OF THE ARPT. WE REQUESTED A SW DEV FROM ZMA; WHICH WAS APPROVED AT OUR DISCRETION. AS WE APCHED W OF THE MTH AREA; WHICH WAS WHERE OUR DEV HAD TAKEN US; I CALLED ZMA TO ADVISE THAT WE INTENDED TO CONTINUE ON OUR SW HDG UNTIL W OF MTH AND THEN TURN INTO MTH; AND THAT I WAS NOT SURE OF THE EXACT LOCATION OF THE STORM -- THAT IT WAS PROBABLY N OF MTH; BUT COULD POSSIBLY BE OVER MTH. HE REPEATED THAT DEVS AT OUR DISCRETION WERE APPROVED. PROGRESSIVELY; WE HAD BEEN STEPPED DOWN TO 2000 FT MSL; AND WERE THEN CLRED DISCRETION TO 1500 FT. SINCE I SAW MARATHON; AND SINCE NO LIGHTNING HAD FLASHED IN A WHILE; I TURNED E; ADVISING THE CTLR OF THE TURN. AS WE LEVELED; I NOTICED AN OBSCURATION OF THE ISLAND LIGHTS TO THE SE; THE CAUSE OF WHICH I ASSUMED TO BE RAIN. AS WE APCHED CLOSER TO MTH; WE ENCOUNTERED HVY RAIN AND A DOWNDRAFT THAT DROPPED US TO 1200 FT MSL BEFORE I COULD STOP THE DSCNT. FEARING A SECOND AND MORE SEVERE DOWNDRAFT; I INITIATED A L TURN; AWAY FROM THE PRECIPITATION THAT I HAD SEEN TO MY R BEFORE WE ENTERED THE RAIN; AND INITIATED A CLB TO RECOVER MTH AND LAND AT EYW. WE WERE STILL IN HVY RAIN AND TURB; AS I CALLED MIA TO ADVISE HIM THAT WE NEEDED TO LAND AT EYW. I WAS TOO BUSY TRYING TO CTL THE ACFT TO GIVE DETAILS SUCH AS MY TURN; AND MY FLT CONDITIONS; AND MY ALT; WHICH WAS NOW 2300 FT. HE OFFERED; AND I ACCEPTED; A VECTOR OF 220 DEGS TO EYW. AS WE CAME OUT OF THE PRECIPITATION AND TURB; ZMA HANDED US TO KEY WEST APCH; WHO IMMEDIATELY CHALLENGED OUR ALT AS BEING A DEV FROM WHAT WAS ASSIGNED AND TO IMMEDIATELY DSND TO 1500 FT. I RESPONDED THAT WE HAD JUST BEEN DEALING WITH SOME SERIOUS WX; IMPLYING THAT CTL OF THE ACFT HAD BEEN DIFFICULT. HE RESPONDED THAT I ONLY HAD TO ADVISE THE CTLR OF THE CHANGE. I ONLY ACKNOWLEDGED THE XMISSION; DECIDING NOT TO GET INTO THE FACT THAT I HAD CALLED MIA TO ADVISE MY NEW INTENTIONS; AND THAT BEYOND THAT; I WAS COMPLETELY INVOLVED IN CTLING THE ACFT. KEY WEST APCH HAD TOLD ME THAT MIAMI REQUESTED HIM TO DISCUSS THE ALT WITH ME; AND I AGREE THAT A MORE COMPLETE RPT OF MY SIT AND RESPONSES TO IT WAS APPROPRIATE; BUT AT THE TIME; MY COMPLETE ATTN WAS FOCUSED ON CTLING THE ACFT; AND SINCE 1500 FT IS ALREADY CLOSE TO THE WATER IN THOSE CIRCUMSTANCES; I WANTED TO MAKE SURE THAT I WAS READY TO DEAL WITH WHATEVER NEXT HAPPENED.