A PIPER ARROW IV PLT FLYING IN MUFH AIRSPACE EXPERIENCED EXTREME WX BUILDUPS; CAUSING A SUDDEN 1000 FOOT ALT DEV.

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WHILE ENRTE FROM MWCR (GRAND CAYMANS) TO EYW (KEY WEST) IN THE MID AFTERNOON; STORMS BEGAN BUILDING AHEAD AND OVER CUBA. THERE WERE SEVERE STORMS TO THE W. ON THE G448 AIRWAY; AND FURTHER TO THE E; THERE WAS A BREAK APPROX 40 NM E OF THE AIRWAY. REQUESTED A DEV TO THE E AND WAS CLRED; EVEN TO PENETRATE RESTRICTED AIRSPACE. APCHING THE COAST OF CUBA; THE OPENING WAS CLOSING QUICKLY SO WE CLBED TO FL10 AND WITH MINOR TURNS; WERE ABLE TO CONTINUE NORTHWARD THROUGH THE GAP. ONCE CLR OF THE INITIAL OPENING IN THE LINE; ANOTHER LINE IN THE MIDDLE OF CUB ISLAND; WHICH HAD TWO CLR AREAS; WAS ALSO TURNING INTO A SOLID LINE. ANOTHER PLANE (NAVAJO) HAD TAKEN OUR PATH ONLY 5 TO 7 MINS BEFORE; BUT; WE QUICKLY FOUND OURSELVES TOTALLY SURROUNDED BY SEVERE STORMS WITH THE EXCEPTION OF ONE AREA OF QUICKLY BUILDING WX WITH TOPS TO ONLY 20000 FT. SLOWING TO MANEUVERING; ASKING FOR DEV FURTHER E TOWARD THE 'SOFT SPOT;' WE PENETRATED THE WX. MODERATE RAIN AND MODERATE TURB ONLY WAS EXPERIENCED BUT THE UPDRAFT OF THIS RAPIDLY BUILDING STORM PUSHED US UP 1000 FT IN APPROX 20 SECONDS. ONCE THROUGH THAT LINE; THE REMAINING TRIP WAS UNEVENTFUL. I FLY IN FLORIDA MOST OF THE TIME AND AM USED TO RAPIDLY DEVELOPING WX; BUT THE RATE OF GROWTH OVER THE CUBAN ISLAND HAS ALWAYS AWED ME. WHILE THE PHENOMENA MAY OCCUR ELSEWHERE; THE SIZE OF CUBA CREATES RAPID STORMS OVER A WIDE AREA. SUGGEST FSS BRIEFINGS FOR GA FLTS OVER CUBA INCLUDE A WARNING TO BEWARE OF EXTREMELY RAPID WX DEVELOPMENTS AND NEED FOR ALTERNATES SHOULD STORMS BECOME UNPASSABLE. AN INTERNATIONAL RCO TO MIAMI FSS; SO WEATHER RADAR INFO COULD BE PROVIDED IN FLT; WOULD ALSO BE USEFUL.