C340 PLT AND HIGH WING SINGLE ENGINE ACFT HAD A NMAC IN ZZZ; US CLASS C. THE PLT THEN PENETRATES RESTR AIRSPACE WITHOUT CLRNC.

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I DEPARTED ZZZ FOR A PART 91 VFR FLT TO ZZZ1. I HAD PLANNED TO FLY GPS DIRECT TO ZZZ1; WHICH WOULD KEEP ME W OF THE RESTR AIRSPACE AROUND THE KENNEDY SPACE CTR. AFTER TAKEOFF I MADE A L 45 DEG TURN TO EXIT THE TFC PATTERN AND SWITCHED FREQ TO ZZZ2 APCH. THE CEILING WAS UNLIMITED; BUT FLT VISIBILITY WAS NOT BETTER THAN 5 MILES IN MIST/HAZE. I ATTEMPTED TO CONTACT ZZZ2 SEVERAL TIMES WHILE I CLIMBED TO 3500 FT MSL AND MANEUVERED TO KEEP CLR OF TFC IN THE VICINITY OF ZZZ AND ZZZ4 PLUS THOSE INBOUND TO ZZZ2. THE FREQ WAS VERY BUSY AS WAS THE TFC IN THE AREA. I SAW A SINGLE ENGINE HIGH WIND PASS DIRECTLY OVERHEAD WITH LESS THAN 500 FT OF SEPARATION WHICH UPSET MY PAX. ZZZ2 APCH FINALLY RESPONDED. I REQUESTED FLT FOLLOWING TO ZZZ1 AT 3500 FT AND THEY GAVE ME TRANSPONDER CODE. I WAS LOOKING VIGOROUSLY FOR TFC AND TURNING TOWARD MY HEADING WHEN MY PAX SAID THEY HAD TFC OFF TO OUR R. I STOPPED MY TURN SHORT AND STARTED TO LOOK FOR THE TFC. NOT LONG AFTER THIS I GOT A CALL FROM ZZZ2 TELLING ME THAT I HAD ENTERED THE KENNEDY SPACE CTR'S (R-2934) RESTR AIRSPACE. I STARTED IMMEDIATE R TURN TO THE N TO EXIT THE AREA. ZZZ2 HANDED ME OFF TO ANOTHER CTLR. I HOLD HIM MY INTENTION WAS TO RTN TO ZZZ. HE TOLD ME I NEEDED TO RTN TO XXX.XX. I CHKED BACK IN AND WAS CLRED BACK TO ZZZ. THE CTLR THEN GAVE ME A PHONE NUMBER TO CALL UPON LNDG. I CALLED THE PHONE NUMBER AFTER EXITING THE ACFT. THE FAA MAN ASKED IF I KNEW OF THE RESTR AIRSPACE. I TOLD HIM I WAS AWARE OF IT; AND TOLD HIM IT WAS COMPLETELY UNINTENTIONAL. I GOT FURTHER E AND S AFTER TAKEOFF THAN I HAD INTENDED AND THEN DUE TO THE INTENSE TFC; FREQUENCY CONGESTION; CONCERN FOR MY PAX STATE OF MIND AND LIMITED VISIBILITY; I LOST MY SITUATIONAL AWARENESS. IN HIND-SIGHT I REALIZE THAT I SHOULD HAVE TURNED TO THE W MUCH SOONER TO RE-INTERCEPT MY ORIGINAL COURSE. I ALLOWED MY CONCERN FOR TFC AVOIDANCE AND PAX COMFORT TO INTERFERE WITH MY NAVIGATION. I HAVE LEARNED A VERY VALUABLE AND HUMBLING LESSON.