ZMP CTLR INVOLVED IN OPERROR DUE TO PREVIOUS INCORRECT FLT PLAN ROUTING AND MISSED ALT CHANGE CAUSING COMPLEX VECTORING WITHOUT THE ABILITY FOR TIMELY ALT CHANGE TO ENSURE SEPARATION.

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HAD JUST RELIEVED ANOTHER CTLR AT RADAR POS. SEVERAL ACFT WERE TRANSITING THE SECTOR WITH OTHERS APCHING SECTOR BOUNDARIES IN HDOF STATUS AND SOME NEEDING TO BE HANDED OFF AND XFERRED TO THE NEXT CTR (ZAU). ACFT #1 WAS IN HDOF STATUS JUST W OF SECTOR BOUNDARY ON AN EBOUND TRACK AND SHOWED DSNDING FROM FL350 TO FL330 IN THE DATA BLOCK. ACFT #2 WAS IN HDOF STATUS JUST S OF SECTOR BOUNDARY NEBOUND ON A CONVERGING COURSE AT FL330. BECAUSE OF OTHER CONFLICTING TFC AT FL350; AND FL310; CLBING TO FL370 OUT OF FL330; AND TIME CONSUMING COORD INVOLVING 4 SECTORS IN THE SW CORNER OF MY SECTOR; IMMEDIATE ALT CHANGES WERE IMPOSSIBLE. BOTH ACFT WERE TURNED TO THE EXTENT POSSIBLE WITHOUT LOSING SEPARATION WITH OTHER TFC AT THE SAME ALT (ANOTHER NBOUND FLT AT FL330) AND ACFT #2 WAS DSNDED AS SOON AS IT WAS CLR OF TFC. HOWEVER; ACFT PASSED WITH ONLY 4.75 NM AND 1000 FT; WHERE 5 NM OR 2000 FT ARE REQUIRED. THIS PARTICULAR CORNER OF AIRSPACE IS VERY ILL DESIGNED AND IN SPITE OF NUMEROUS INCIDENTS IN IT; MGMNT REFUSES TO MAKE MINOR CHANGES THAT WOULD SOLVE MOST PROBS. SUPPLEMENTAL INFO FROM ACN 541670: A CONTRIBUTING FACTOR WAS SECTOR 17 CTLR HAD TAKEN OVER THE RADAR POS ABOUT 7 MINS BEFORE INCIDENT. DURING THIS TRANSITION; THE REVISED ALT WAS MISSED; SO ACR X STRIP STILL SHOWED FL370. ALSO; ACR Y SHOULD NOT BE ON FOD TRANSITION; BUT DIRECT MCW; KASPR 2 ARR. FOD TURNS THE ACFT NW; THEN NE INTO THE VERY SE TIP OF SECTOR 17; THE 'COFFIN CORNER.' THIS WAS TO BE ELIMINATED 6 MONTHS AGO; BUT NO ACTION YET. NO ONE WHO WORKS SECTOR 17 LIKES THESE ACFT ON THE FOD TRANSITION.