BAE3100 ACFT HAS R ENG PROP GO INTO FULL REVERSE DURING APCH INTO JLN. ACFT WAS UNCONTROLLABLE UNTIL PROP WAS FULLY FEATHERED.

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AFTER BEING RADAR VECTORED ON LOC BACK COURSE RWY 31 AND UPON INTERCEPTING THE LOC WE WERE CLRED TO TWR AND CLRED TO LAND. WHILE STILL IMC MY R ENG UNCOMMANDED WENT INTO BETA MODE AND SUBSEQUENT FULL REVERSE WITH THE APPLICATION OF MAX PWR. MAKING A GAR/MISSED APCH IMPOSSIBLE AND ACFT CTL SEVERELY UNMANAGEABLE UNTIL R ENG WAS FEATHERED. WHILE ENG WAS BEING SECURED WE ADVISED TWR THEN ZKC OF OUR INTENTIONS TO CLB TO 4000 FT AND WE WANTED TO DIVERT TO SGF. I ELECTED TO DIVERT TO SGF WHICH COULD ACCOMMODATE A PRECISION APCH WITHOUT HAVING A TAILWIND AND COULD PROVIDE APCH RADAR CTL THROUGHOUT THE APCH. NOT ONLY WAS I THINKING OF THE FACTORS; BUT ALSO THE IMPROVING WX CONDITION AT SGF AND THE FACT THAT THIS REGIONAL ARPT PROVIDED BETTER CRASH/RESCUE EQUIP IN CASE IT BECAME NECESSARY. SOME OF THE FACTORS CONTRIBUTING TO MY DECISIONS WERE MY FO LACK OF EXPERIENCE AND THE FIRST FLT WE EVER FLEW TOGETHER. THE TIME WE NEEDED AS A CREW TO EFFECT THE SAFEST POSSIBLE APCH AND LNDG. THE ABILITY FOR SGF TO PROVIDE BETTER RADAR COVERAGE THROUGHOUT THE APCH. THE WINDS AND WX BETTER AND MORE SUITABLE FOR THE PRECISION APCH WITH FULL FLAPS AND LIFT PUMP UNAVAILABLE AND OF COURSE THE ABILITY FOR SGF TO PROVIDE BETTER RESCUE EQUIP. ALL OF THIS WAS APPROVED BY MY COMPANY'S FLT CTL. BY DIVERTING TO SGF I USED MY PIC EMER AUTH TO EFFECT WHAT I FEEL TO BE THE SAFEST POSSIBLE APCH AND LNDG. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: ON APCH TORQUE WAS SET TO ABOUT 40%; IT SLOWLY DECREASED TO 20% AND THEN INTO BETA RANGE RESULTING IN FULL REVERSE ON THE R-HAND ENG. PLT ALMOST LOST FULL CTL OF THE ACFT WHILE THE ENG IN REVERSE WAS BEING SHUT DOWN. RPTR THOUGHT THE ENG HAD A FLAMEOUT UNTIL HE SAW THE BETA LIGHT ON. CONFIRMATION THAT THE ACFT WAS IN REVERSE WAS THE ACFT FELT READY TO ROLL OVER; YET THE ENG HAD HIGH RPM. THIS ALSO CONFIRMED THE ENG WAS IN REVERSE. RPTR STARTED A GAR BY RETRACTING THE LNDG FLAPS TO 10 DEGS. THE ACFT WANTED TO ROLL; PLT APPLIED ALL CTL SURFACES FULLY TO KEEP ACFT IN PROPER ATTITUDE. BY THE TIME THE R-HAND ENG WAS SECURED; CONTROLLABILITY OF THE ACFT BECAME EASIER FOR THE PLT. AIRSPD DURING ALL THIS WAS V2. PLT THEN DECIDED TO FLY THE ACFT OVER TO SGF TO GAIN ACCESS TO A LONGER RWY; BETTER WX; AND BETTER CFR. LATER; THE NEWS MEDIA QUERIED HIM ABOUT FLYING OVER TO SGF. THE MEDIA INFERRED THAT BY HIS FLYING TO SGF; THE JLN ARPT IS AN UNSAFE ARPT. UPON LNDG AT THE SGF ARPT; COMPANY MAINT INSPECTED THE ENG AND FOUND THE PROP GOVERNOR HAD FAILED. IT WAS REPLACED THE NEXT DAY AND THE FLC FLEW THE ACFT AWAY FROM SGF AND BACK INTO SCHEDULED SVC.