ACR-WDB CLEARED SOUTHEASTBOUND ON A300 AND ACR-LGT CLEARED NORTHWESTBOUND ON A300; BOTH AT FL290; RESULTING IN NMAC AND LESS THAN STANDARD SEPARATION.

Narrative

I TOOK OVER THE POS (D4) WITH A TRNEE AT XX38Z. AT THAT TIME THE NBOUND RUSH WAS STARTING AND WE FOUND OURSELVES RUNNING OUT OF NBOUND ALT (RIGHT ALT FOR DIRECTION OF FLT). I REQUESTED FL370 FOR WDB Z ON A300 AND WAS DENIED BY THE NEW YORK CTLR. DURING THE RUSH I HAD TFC NBOUND AT FL280 (LGT Y) AND ANOTHER BEHIND HIM (LGT W); ALSO REQUESTING FL280 OR FL310. FL310 WAS UNABLE DUE TO WDB T AT THAT ALT. THE ONLY CHOICE FOR LGT X WAS FL260; UNLESS I COULD GET APPROVAL FROM NEW YOUR CENTER FOR A HIGHER ALT WRONG FOR DIRECTION. I SCANNED THE BAY TO SEE IF THEIR WAS ANY TFC SBND AT FL290 AND ONLY OBSERVED ONE; LGT V; WHICH WAS ESTIMATING LENNT AT XY11Z. LGT Y WAS ESTIMATING LENNT AT XY15Z. I CALLED NEW YORK CENTER AND REQUESTED FL290 FOR LGT Y. AT THAT TIME IT WAS APPROVED WITH NEITHER NEW YORK CTLR NOR MYSELF RECOGNIZING THE POTENTIAL CONFLICT WITH WDB X. I INFORMED THE RADAR PERSON THAT FL290 WAS APPROVED REF LGT V OBSERVED ON RADAR. I WAS INFORMED ABOUT THE NEAR MISS BTWN WDB X AND LGT Y AT XY49Z BY COM RADIO. AT THE TIME OF THE INCIDENT I WAS WORKING APPROX 25 ACFT. I COULD ONLY RECOMMEND THAT A FLOW RESTRICTION BE APPLIED TO RELIEVE THE STRESS. SUPPLEMENTAL INFO FROM ACN 87769: FLYING NBOUND FROM SJU TO PHL; THE CREW AND I ENCOUNTERED A NMAC WITH A SBND FLT. WE WERE BOTH CLRED THE SAME ROUTE AND FLT LEVEL BY 2 DIFFERENT ATC FACS. THE SBND ACFT PASSED 300' OFF OUR STARBOARD WING. ATC WAS IMMEDIATELY NOTIFIED.