AFTER LONG FLT; FLC FATIGUED; CLRED FOR CAT II III APCH; VECTORED AT 4000 FT JUST OUTSIDE OF OM. IN ORDER TO DSND TO GLIDE PATH; FLC HAD TO USE EXCESSIVE DSCNT; CLOSE IN; WHICH SET OFF GPWS. FLC EXECUTED GAR AND BACK FOR ANOTHER UNEVENTFUL APCH. WX WAS LOWER THAN RPTED BY ATIS AND APCH CTL.

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CAME BACK TO COCKPIT FROM REST BREAK TO FIND JFK CALLING CAT II/III WX TO RWY 04; BNA AS ALTERNATE. AFTER 11 HR FLT. ATC WAS CALLING FOR WX CAT II/III RWY 04. ON OUR VECTORS TO RWY 04 ATC SWITCHED TO RWY 31R AND CALLED WX AS 400 FT; 1 MI VIS. THEY DIDN'T TELL US RWY 04 LOC WENT OTS DURING OUR VECTORS TO RWY 04 OR RWY 31R. CLRED FOR APCH TO RWY 31R WITH 4000 FT LOC INTERCEPT JUST OUTSIDE THE OM; WE SET UP A STEEP GRADUATED RATE OF DSCNT MANUALLY WITH VERT SPD TO INTERCEPT GS FROM ABOVE; INTERCEPTING GS AT 400 FT WITH 800 FT RATE OF DSCNT; GOT THE GPWS TERRAIN WARNING; INITIATED MANUAL GAR FOLLOWING V-BARS WITH 3000 FPM RATE OF CLB. AT 1500 FT ATC ADVISED TO LEVEL AT 2000 FT. BEAR IN MIND WE NEVER BROKE OUT AT 400 FT. ALSO PUBLISHED MISSED APCH CALLS FOR 4000 FT; NOT 2000 FT. WITH THE HIGH RATE OF CLB; GAR PWR; MANUAL CTL GAR; HIGH NOSE ATTITUDE; WE BUMPED PAST 2000 FT TO 2300 FT THEN BACK DOWN TO 2000 FT. ACCEPTED ANOTHER VECTOR TO RWY 31R AT 2000 FT WITHOUT INCIDENT; BUT BROKE OUT AT 200 FT AND 1/2 MI; NOT THE 400 FT 1 MI VIS THEY INSISTED IN GIVING US FOR RWY 31R. NO RVR WAS EVER RPTED. ATC NEEDS TO BE MORE AWARE OF ACFT TYPE THEY ARE CTLING; ACFT PERFORMANCE; DON'T SET US UP 2000 FT ABOVE THE NORMAL GS INTERCEPT ALT. DON'T SET US UP TO INTERCEPT THE GS FROM ABOVE THAT CLOSE IN TO OM; RPT THE REAL TIME WX AND NOT SCAM US WITH WX THAT ACCOMMODATES THEIR CHOICE OF RWYS. PROVIDE REAL WX NOT BOGUS WX GUESS; REALIZE ALSO THAT THE CREW IS COMING OFF A 10-11 HR FLT AND CREW FATIGUE. AND WORKLOAD COMBINATIONS WITH WX.