GO AROUND ADVISED #1 FOR RWY 1 ENCOUNTERED MLG ON STRIAGHT IN FOR RWY 1.

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MCI TWR ISSUED US GO AROUND INSTRUCTIONS BECAUSE OF ACFT ON RWY AHEAD OF US (RWY 27). WERE TOLD TO TURN LEFT FOR RIGHT DOWNWIND RWY 1. I TURNED TO 190 DEG HDG; THEN CALLED FOR BALKED LNDG CHK. F/O COMPLIED WHILE I SET UP LOC FOR RWY 19. WE NEXT ASKED MCI TWR TO VERIFY WE WERE CLRED TO LAND RWY 1. WE WERE URGENTLY TOLD YES; TO TURN BASE NOW; THAT WE WERE #1 WITH AN ACR MLG; #2 BEHIND US ON LEFT BASE. WE WERE INSIDE RWY 1 LOM; BUT I HAD NO IDEA HOW CLOSE TO THE FINAL PATH. IMMEDIATELY I STARTED A RIGHT TURN TO BASE; LOOKING FOR THE MLG AHEAD AND TO MY LEFT; THE ASSUMED LOCATION FOR AN ACFT ON LEFT BASE LNDG BEHIND US. TWR HAD GIVEN US NO LOCATION INFO ON THE MLG. AS WE CROSSED THE FINAL APCH PATH TO RWY 1; APPROX 20 DEGS SHORT OF A 90 DEG BASE HDG; MY F/O SPOTTED THE MLG AT OUR ALT AT OUR 1 O'CLOCK POS; SAME ALT. WE WERE TURNING DIRECTLY INTO HIM AS HE WAS ON BASE TURNING ONTO FINAL. THE MLG SAW US AT SAME TIME AND TOLD TWR WE WERE TURNING INTO HIM. TWR NEXT TOLD MLG TO TURN RIGHT; WHICH WOULD HAVE BEEN INTO US; AND TOLD US TO CONTINUE OUR RIGHT TURN ONTO FINAL DIRECTLY INTO THE MLG. MLG WAS BTWN US AND THE ARPT; TURNING FINAL. WE WERE XING FINAL IN OPPOSITE DIRECTION TO HIM. THESE TWR INSTRUCTIONS WOULD HAVE COLLIDED US. I IMMEDIATELY STOPPED OUR RIGHT TURN AND MADE A 270 DEG LEFT TURN BACK TO FINAL WHILE MLG CONTINUED HIS LEFT TURN TO FINAL. BOTH MLG AND MY ACTIONS WERE THE ONLY ACTIONS AVAILABLE TO PREVENT A MIDAIR; WHICH WERE BOTH OPP WHAT THE CTLR HAD ISSUED. WE PASSED APPROX 300' FROM EACH OTHER AT SAME ALT. BOTH ACFT WERE ACR'S WITH OPERABLE MODE C; BOTH TALKING TO SAME CTLR. CTLR STILL DID NOT KNOW OUR RELATIVE POSITIONS; (I.E.; THE CTLR TWICE ISSUING COLLISION COURSE VECTORS). I MUST QUESTION THE WISDOM OF THE NEW FAA MANDATE FOR NEW MODE C REQUIREMENTS. IT DIDN'T WORK HERE. RATHER; RE-HIRE OLD AVAILABLE CTLRS TO HELP ALLEVIATE THE CURRENT EXCESSIVE CTLR WORKLOAD SITUATION.