ACR MLG OVERSHOT ALT RESULTING IN LESS THAN STANDARD SEPARATION WITH MTR.

Narrative

DURING CLBOUT FROM CVG WE WERE APPROX 13000-14000' CLBING TO 23000'. WE WERE GIVEN A CHOICE OF DIRECT HMV WITH RESTRICTION TO 19000' OR CLB TO CLRED ALT WITH VECTORS. CAPT ELECTED TO GO DIRECT AND THE NAV COMPUTER REPROGRAMMED FOR DIRECT HMV. TFC WAS CALLED AS A MTR AT 20000' WBOUND; 12 O'CLOCK. SEARCHING FOR TFC KEPT MY EYES OUTSIDE; THOUGH THE 18000' SWITCH TO 29.92 WAS ACCOMPLISHED. WE HAD NOT; HOWEVER; RESET THE TARGET ALT ON THE ALT ALERTER. DUE TO THE HIGH RATE OF CLB THE ACFT GENERATES; WHEN I REALIZED AN OVERSHOOT HAD TAKEN PLACE IT WAS ALREADY TOO LATE TO PREVENT AN OVERSHOOT W/O TAKING EXCESSIVELY ABRUPT ACTION. I OBSERVED THE MTR PASSING OFF OUR RIGHT WING. MY PREVIOUS FORMATION EXPERIENCE ON THAT ACFT WOULD SUGGEST A 2000' SEP AT CLOSEST POINT. IN THIS EVENT; THE ACT OF SETTING THE NEW DEST IN THE COMPUTER (OR MORE EXACTLY; WATCHING THE CAPT DO THIS) LEFT ME MENTALLY SATISFIED THAT THE ALT WAS ALSO CURRENT. AS A RESULT; I PAID MORE ATTN OUTSIDE THAN INSIDE WHEN THE ASSIGNED ALT PASSED. SUPPLEMENTAL INFO FROM ACN 88999: BY THE TIME I NOTICED US AT 18800' AND CLBING AT ABOUT 3500 FPM; WE ROUNDED OFF ABOUT 20000' BEFORE I COULD START BACK TO 19000' W/O CAUSING AN UNCOMFORTABLE NEGATIVE G ON THE PAX.