SEPARATION LOST WHEN CPR-LTT OVERSHOT CLIMB TO FL290 AND CONFLICTED WITH AN ACR-LGT AT FL310.

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ON DEP FROM NEW ORLEANS LAKEFRONT; WE WERE STEP CLBED TO FL290. AT ALT WE WERE CLBING 3 LAYERS OF HIGH ALT CLOUDS THAT WERE FEEDING INTO HURRICANE GILBERT. WE WERE ENCOUNTERING CONTINUOUS LIGHT; OCCASIONALLY MODERATE CHOP. AS WE CLBED THROUGH FL280 AND RECEIVED OUR ALT ALERTER (1000' TO GO) WARNING; I BECAME AWARE THAT WE WERE BEGINNING TO PICK UP RIME ICE AT A RAPID RATE. I BEGAN CHKING TO SEE THAT ALL ANTI-ICE/DE-ICE SYSTEMS WERE ON AND OPERATING. AT THIS SAME TIME; CENTER WAS CLRING US DIRECTION TO GREENWOOD VOR AND ISSUING A TFC ADVISORY. I BECAME DISTRACTED BY THE ICING CONDITIONS AND THE COPLT WAS DISTRACTED TRYING TO LOCATE THE GREENWOOD VOR FREQ. I REALIZED THAT I WAS ABOVE MY ASSIGNED ALT AT ABOUT 29700' AND BEGAN MY DSCNT BACK TO FL290 AT THE SAME TIME THE CTLR WAS POINTING OUT THE DEVIATION. HUMAN PERFORMANCE: I FIXATED ON THE ICING PROB BRIEFLY AND SHOULD HAVE BEEN FLYING THE AIRPLANE. I WAS USED TO FLYING ACFT WITH ALT PRESELECT/LEVEL OFF FEATURES ON THE AUTOPLT AND THIS ACFT DID NOT HAVE THIS FEATURE. EVEN THOUGH THE LEVEL OFF FEATURE STILL REQUIRES MONITORING TO SEE THAT IT FUNCTIONS PROPERLY; IT DOES REDUCE WORKLOAD SIGNIFICANTLY IN A HIGH PERFORMANCE ACFT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: RPTR MADE A FOLLOWUP TELEPHONE CALL TO A ZME SUPVR. THE SUPVR INFORMED RPTR THAT A COMPUTER DETECTED LOSS OF SEP OCCURRED AND THAT ALL THE EVIDENCE WOULD BE FORWARDED TO FSDO. RPTR HAS SINCE HEARD THAT AN INVESTIGATION IS BEING CONDUCTED BY FSDO. NOTHING MORE HAS TRANSPIRED. RPTR ADMITTED THAT HE WAS DISTRACTED BY THE ICING PROB AND DID NOT PAY ENOUGH ATTN TO THE LEVEL OFF PROCESS. NOT HAVING A FLT DIRECTOR WITH ALT CAPTURE ON THAT ACFT WAS A CONTRIBUTING FACTOR.