A B767-300 FLC OVERSHOOTS THEIR MISSED APCH ALT AFTER TWR ASSIGNS AN ALT FOR A MISSED APCH OTHER THAN THAT PUBLISHED AT ATL; GA.

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ATL APCH VECTORED US ONTO A VISUAL APCH FOR RWY 27L IN ATL WITH NIGHT VMC CONDITIONS. THERE WAS MINIMUM SEPARATION BETWEEN US AND THE 2 ACFT AHEAD OF US. AWARE OF THIS; WE WERE SLOWED TO VERY NEAR OUR FINAL APCH SPD AND THE SEPARATION WAS STILL A CONCERN TO US. AFTER SWITCHING TO TWR; FULLY CONFIGURED AND WITH CLRNC TO LAND; WE QUESTIONED THE CTLR ON OUR SEPARATION WITH THE ACFT AHEAD. AT THIS TIME THE CTLR STATED 'THIS ISN'T GOING TO WORK' AND INSTRUCTED US TO GAR. I WAS FLYING THE ACFT WITH THE AUTOPLT OFF AND THE GAR WAS FLOWN MANUALLY (AUTO THROTTLES DISCONNECTED). PUBLISHED MISSED APCH ALT WS 3500 FT AND WAS BRIEFED AND SET IN MODE CTL PANEL ALT WINDOW. IN HINDSIGHT I REALIZE THE CTLR TOLD US TO CLB TO 3000 FT. I INITIATED THE GAR AT APPROX 1800 FT MSL AND WAS INSTRUCTED TO TURN LEFT TO 180 DEGS. AS WE WERE RAISING GEAR; RECONFIGURING FLAPS; ADDING PWR; TURNING AND CLBING; THE CTLR UPDATED OUR HDG TO 120 DEGS. THE CAPT WAS MAKING A PA TO THE PAX; AND I REACHED UP TO UPDATE THE HDG BUG AND RESPOND TO THE CTLR. I THEN NOTICED US CLBING THROUGH 3500 FT (THE PUBLISHED ALT). I IMMEDIATELY BEGAN TO ARREST THE CLB AND DSND BACK TO 3000 FT. I BELIEVE WE 'TOPPED OUT' AT 3800 FT. THE CTLR THEN INSTRUCTED US TO MAINTAIN 3500 FT. THERE WAS NO KNOWN CONFLICT OR REMARKS FROM THE CTLR; WE CAME BACK AROUND FOR ANOTHER VISUAL AND LNDG ON RWY 27L. WE FAILED TO AVIATE NAVIGATE AND THEN COMMUNICATE. THE PA SHOULD HAVE WAITED UNTIL LEVEL OFF AND /OR AUTOMATION RESTORED. ADD TO THIS A VERY LIGHT; PWRFUL ACFT WITH OVER 1200 FT TO CLB WHILE TURNING; RECONFIGURING AND TALKING AND YOU HAVE AN ALT DEV. PRIORITIZE AND FLY THE AIRPLANE!