2 ACFT HAD TO TAKE EVASIVE ACTION GAR BECAUSE OF AN ACFT ON THE RWY.

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CLRED FOR A VOR/DME 22L APCH AT JFK. KEPT HIGH ON VECTORS; ARRIVED AT FINAL APCH FIX AT 1500 FT MSL. CLRED TO LAND #3 ON APCH FOR RWY 22L. TYPE OF ACFT AHEAD NOT IDENTED. AT APPROX 3 MI FROM TOUCHDOWN; 1000 FT MSL ACFT STILL ON RWY. CAPT INITIATED A GAR. AT THE SAME TIME; ACFT AHEAD THAT HAD BEEN #2 TO LAND ALSO WAS ON A MISSED APCH GAR. AT NO TIME DID WE HAVE THE PRECEDING ACFT IN SIGHT; NOT DID THE TWR CALL TFC TO US. TCASII WAS NO HELP. THE COCKPIT WORKLOAD INCREASED AS WE LOOKED FOR OTHER ACFT AS WE WENT AROUND. WE ENTERED IMC. AT ABOUT 2500 FT MSL; CONSIDERABLY BEHIND THE CURVE; DISTRACTED BY UNRPTED AND UNSEEN TFC. VECTORING FOR RWY 13L; THERE WAS CONFUSION REGARDING TYPE OF APCH WE WERE CLRED FOR WITH APCH TRYING TO SUGGEST A VISUAL BY ASKING US REPEATEDLY FOR OUR PREVAILING VISIBILITY (IT WASN'T GOOD ENOUGH FOR A VISUAL). WE GOT CAUGHT UP; SHOT THE APCH AND LANDED. LESSONS: APCH IN ITS EFFORT TO SQUEEZE ARRS SHOULDN'T PRESS INTL HEAVIES ONTO ARRIVING DOMESTIC ACFT. TWR SHOULD SEE THAT 2 ACFT ON SAME RWY EXECUTING A GAR AT SAME TIME DESERVE THE TWR'S ATTN FOR SEPARATION. WE COULD HAVE USED MORE HELP. APCH CTL; TRYING TO BE HELPFUL; CONFUSED THE SIT WITH ITS ASKING ABOUT VISUAL CONDITIONS.