PC-12 FLT CREW WAS GIVEN RWY CHANGE WHILE ON VECTOR FOR THE LOC FOR THE PARALLEL RWY. THE FLT WAS INSTRUCTED TO GO AROUND AND GIVEN A SHORT APCH WHICH RESULTED IN A HIGH; UNSTABILIZED APCH AND LONG LNDG.

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WE WERE ON AN IFR FLT PLAN TO JFK. THE WX AT JFK WAS SOLID IFR; BUT THE MINIMUMS ON THE ILS WERE ADEQUATE TO ALLOW FOR A LNDG. WE LISTENED TO THE ATIS AND PREPARED FOR THE ILS RWY 31R. UPON CONTACTING THE FINAL APCH CTLR WE WERE TOLD TO EXPECT VECTORS TO ILS RWY 31R. THE CTLR; WHO WAS IN TRAINING; ISSUED US SEVERAL VECTORS AND THEN GAVE US A HDG TO INTERCEPT THE LOC FOR RWY 31L. WE QUESTIONED ILS RWY 31L AND WERE TOLD THAT WE SHOULD NOW EXPECT ILS RWY 31L. WE QUICKLY SET UP AND BRIEFED THE APCH FOR RWY 31L. WE WERE TOLD TO MAINTAIN MAX FORWARD AIRSPD AND CLRED FOR THE APCH. JUST BEFORE THE FAF WE WERE SWITCHED TO THE TWR FREQ. THE TWR CTLR GAVE US A HDG AND ALT TO FLY BUT NEVER CANCELED OUR APCH CLRNC. AFTER MULTIPLE VECTORS WE WERE SWITCHED BACK TO THE APCH FREQ. BOTH THE CTLR IN TRAINING AND THE INSTRUCTOR CTLR ISSUED SEVERAL CONFLICTING HDGS AND AIRSPDS. OUR SPDS WERE VARYING BTWN 150 KTS AND 210 KTS. AT THIS TIME ANOTHER ACFT CAME ONTO THE FREQ AND DECLARED A 'MAJOR' MEDICAL EMER. THIS SEEMED TO OVERWHELM BOTH OF THE CTLRS WORKING THE FREQ. WE WERE GIVEN A VECTOR TO JOIN THE ILS THAT INTERCEPTED THE LOC OVER THE FAF AND TOLD TO MAINTAIN MAX FORWARD AIRSPD. THE GS WAS ALREADY BELOW CTRED BEFORE THE LOC CAME ALIVE. I WAS HIGH AND VERY FAST ON FINAL AND ACCOMPLISHED ALL OF THE BEFORE LNDG CHKS WELL BEYOND THEIR NORMAL COMPLETION POINT. NORMALLY I WOULD HAVE USED ONLY 2000-3000 FT OF RWY TO LAND. HOWEVER; I LANDED OVER 1/2 WAY DOWN THE RWY AND AT A GREATER THAN NORMAL AIRSPD. AT NO POINT WAS I BELOW GS AND AT NO POINT WAS I OFF COURSE OR IN DANGER OF HAVING INADEQUATE RWY REMAINING. HOWEVER; THE SITUATION WAS VERY FAR FROM IDEAL AND PROFILES AND PROCS WERE NOT FOLLOWED CORRECTLY. I SHOULD HAVE EXECUTED A MISSED APCH AT THE FIRST SIGN OF SOMETHING BEING WRONG. I HESITATED TO DO SO BECAUSE AT THAT POINT I FELT THAT THE SAFEST PLACE WAS ON THE RWY. DUE TO TFC CONGESTION; MEDICAL EMERS AND CTLR INCOMPETENCE I DID NOT FEEL THAT A MISSED APCH WAS SAFE. IN HINDSIGHT; I SHOULD HAVE GONE MISSED AND CONTINUED TO A DIFFERENT ARPT.