KING AIR C90 PLT PENETRATES RESTR AIRSPACE WHEN ATTEMPTING TO AVOID SEVERE TSTMS AND DEP CTLR COULD NOT TURN ACFT THROUGH RESTR AIRSPACE.

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AT APPROX XA30; I DEPARTED RDU AIRSPACE AT 10000 FT MSL AND MADE POSITIVE CONTACT WITH FAY APCH (MY ON-COURSE HDG WAS 210 DEGS). I STATED TO APCH CTL THAT I BELIEVED I WAS GOING TO HAVE TO TURN E OR W TO AVOID THE RESTR AIRSPACE AT FT BRAGG. ATC REQUESTED THAT I FLY HDG 180 DEGS. I ADVISED HIM THAT I COULD TURN ABOUT 190 DEGS DUE TO TSTMS BEING 'PAINTED' ON MY RADAR. HE ADVISED OK. AFTER A FEW MINS OF NAVING ALONG SEVERAL TSTMS ALONG MY L SIDE; ATC ADVISED ME TO CHANGE FREQS. I DID. BY THIS TIME; I HAD ADJUSTED MY RADAR SEVERAL TIMES TO SELECT A SAFE RTE TO CONTINUE ALONG. I WAS ALSO CLRING MY STORM SCOPE TO FURTHER ENHANCE MY DECISION. BY NOW; THE RTE (190 DEGS) WAS GOING TO PLACE THE ACFT INTO A TSTM. I ADVISED ATC OF MY ISSUE AND SHE RESPONDED THAT I COULD NOT TURN TO THE W DUE TO R5311 AT FT BRAGG. I WAS PAINTING SEVERAL INTENSE TSTMS TO MY FRONT AND L AND THERE WAS NO POSSIBLE WAY OF FLYING AROUND THESE TSTMS. KEEP IN MIND THAT IT WAS VMC AT MY CURRENT LOCATION AND TO MY R. I MADE SEVERAL ATTEMPTS WITH ATC WITH LONG PAUSES AND ADVISED HER THAT I WAS MAKING A TURN TO THE R AND CLB ABOVE A SINGLE VERT CUMULONIMBUS (IN VMC). BEFORE I MADE THE TURN; I ALSO CHKED MY ON-BOARD TCASII. BY NOW; AN ARGUMENT ENSUED ABOUT THE LOCATION OF R5311 AND ITS CONTENTS AND ACTIVITIES. I INFORMED HER THAT I WAS FAMILIAR WITH R5311; BUT I DID NOT DESIRE TO RISK GOING THROUGH SEVERAL TSTMS (SAFETY). I TURNED THROUGH A WESTERN HDG TO 360 DEGS FOR A SECOND THEN ON TO AN EASTERLY HDG. I ALSO LEVELED OUT AND THEN DSNDED BACK DOWN TO 10000 FT MSL. I THEN CLRED FAY TO THE S. MY CONCERN; CHANGE OF FREQ WHILE ON VECTOR FROM ATX SO CLOSE TO RESTR AIRSPACE. ARGUMENTS WITH ATC OVER COPYING THE TELEPHONE NUMBER FOR ATC WHILE THE PLT IS TRYING TO EXIT RESTR AIRSPACE. ACFT/PAX SAFETY IN AND AROUND TSTM.