ARTCC RADAR CTLR; IMPACTED BY TFC AND WX AVOIDANCE; BECOMES UNABLE TO LATERALLY SEPARATE CLBING TFC FROM OTHER WX DEVIATING TFC. CTLR RECOGNIZES; AFTER THE FACT; OTHER CTL OPTIONS HE SHOULD HAVE CONSIDERED. CTLR BELIEVES LAST MOMENT ACTIVATION OF CONFLICT ALERT WAS CAUSED BY ACR USAGE OF ICAO IDENTIFIERS IN DATA BLOCK.

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THE SECTOR WAS IMPACTED WITH WX. CTR RADAR IS VERY LIMITED IN DEPICTING WX PHENOMENA. ACFT #1 WAS IN LEVEL FLT AT FL310; SBOUND. ACFT #2 WAS CLBING TO FL330; NBOUND AND DEVIATING W FOR AN UNDETECTED TSTM. THE ACFT WERE INITIALLY SEPARATED LATERALLY. ACFT #2 DEVIATED FURTHER W THAN I ANTICIPATED. WHEN I REALIZED LATERAL WAS NOT AN OPTION ANYMORE; I TRIED TO UTILIZE VERT; BY EXPEDITING ACFT #2'S CLB. I COULD NOT STOP ACFT #2 AT FL280 FOR ANOTHER SBOUND ACFT. FL290 WAS NO GOOD AS I HAD ANOTHER NBOUNDER DEVIATING AND ACFT #1 WAS AT FL310. SO I CONTINUED ACFT #2 TO FL330. I TURNED ACFT #2 E AS SOON AS I COULD; BUT THERE WAS WX INVOLVED AND I WASN'T SURE HE WAS CLR OF IT YET. I TURNED AND DSNDED ACFT #1 AS SOON AS HE WAS CLR OF THE NBOUND TFC AT FL290. ACFT #2 ADVISED THAT HE HAD ACFT #1 IN SIGHT. SEPARATION WAS LOST. CLOSEST PROX WAS 4 NM AND 1700 FT. WHEN SEPARATION WAS RE-ESTABLISHED; I CLRED BOTH ACFT BACK ON COURSE. IN HINDSIGHT; I SHOULD HAVE STOPPED ACFT #2 AT FL270 INITIALLY; HOWEVER; THERE WERE A LOT OF OTHER CONTRIBUTING FACTORS. MIA APCH WAS IN NEED OF 20 MI IN- TRAIL DUE TO WX. THE FOWEE ARR INTO MIA WAS CLOSED DUE TO WX AND WE WERE SEQUENCING THOSE ARRS OVER THE HEATT STAR. SEVERAL ACFT WERE DEVIATING AROUND SEVERAL DIFFERENT TSTMS WITHIN MY SECTOR. THE LACK OF WX RADAR MADE IT DIFFICULT TO ANTICIPATE WHERE THESE VARIOUS ACFT WERE GOING. LASTLY; THE CONFLICT ALERT WAS DELAYED IN ACTIVATING BECAUSE ACFT #2'S MODE C HAD 'TRIPLE X'ED.' THIS HAS BEEN A PROB EVER SINCE WE STARTED USING THE ICAO IDENTIFIERS. THE COMPUTER HAS TROUBLE KEEPING UP FOR SOME REASON.