B737 FLT CREW OVERSHOT ALT ON DEP WHILE SIMULTANEOUSLY LOADING ROUTE CHANGE INTO FMS. RPTR CITES FATIGUE AS CONTRIBUTORY.

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WE PUSHED BACK FROM OUR GATE AT LGA 10 MINS EARLY; ALL CHKLISTS AND PREPARATIONS COMPLETED. OUR TAXI OUT WAS RELATIVELY SHORT FOR LGA (WE WERE ABOUT #6 IN LINE FOR TKOF). WHILE TAXIING TO RWY 31 (#5 FOR DEP); WE WERE TOLD TO CALL CLRNC FOR A RERTE. WE DID SO; AND WERE GIVEN A FULL RTE CHANGE. WE QUICKLY UPDATED OUR FMS DATA; BUT I ASKED MY FO TO CONTACT DISPATCH TO MAKE SURE OUR FUEL LOAD WAS ADEQUATE FOR THE RERTE; ACR COMPANY PROCS. MEANWHILE; WE MOVED UP TO #1 FOR THE RWY. I CALLED THE DISPATCHER ON MY CELL PHONE TO TRY TO GET A QUICKER ANSWER; BUT IT WAS NOT QUICK ENOUGH. WE ASKED LGA TWR FOR EXTRA TIME TO CONFIRM WITH OUR DISPATCHER; BUT WE WERE TOLD TO TAXI R ON TXWY Z AND BACK AROUND ON TXWY A TO HOLD SHORT OF TXWY V AND RPT READY. AS SOON AS WE HAD THE BRAKES SET; OUR DISPATCHER CONFIRMED THAT WE HAD ENOUGH FUEL FOR THE RERTE. WE CALLED READY AND GOT BACK IN LINE AND PERFORMED A ROLLING TKOF (FO FLYING) DUE TO TFC ON A 3 MI FINAL FOR RWY 22. SO FAR; A VERY HECTIC BUT OTHERWISE 'NORMAL' (FOR LGA) DEP. AFTER CONTACTING DEP CTL; WE WERE GIVEN CLRNC TO CLB TO 12000 FT AND A VECTOR TO THE W. WE WERE GIVEN ANOTHER HDG CHANGE; FOLLOWED BY A FREQ CHANGE. AFTER CHANGING FREQS; WE WERE GIVEN A CLRNC TO COL VOR DIRECT WHITE (COL WAS NOT ON OUR FLT PLAN; SO IT WAS NOT LOADED INTO THE FMS). WHEN I ENTERED COL INTO THE FMS; 5 POSSIBLE CHOICES CAME UP. I MUMBLED SOMETHING ABOUT 'THIS MUST BE THE ONE.' WHILE CONFIRMING THE ENTRY ON THE FMS; I HEARD THE ALTDEV WARNING; AND LOOKED UP TO SEE THAT WE HAD OVERSHOT OUR ALT BY ABOUT 300 FT (THAT WAS THE MAX DEV). RIGHT AFTER THAT; NYC DEP TOLD US TO MAINTAIN 12000 FT AS WE WERE RETURNING TO OUR ASSIGNED ALT. WE DID SO; AND THE REST OF THE FLT PROCEEDED NORMALLY. APPARENTLY; MY FO HAD BEEN DISTR BY MY 'MUMBLING' ABOUT THE COL VOR CHOICES AND HAD LOOKED OVER TO HIS SID CHART TO HELP ME OUT JUST BEFORE LEVELOFF. FORTUNATELY; THE AUTOTHROTTLE WAS ENGAGED; SO WE DIDN'T GO BLASTING UP ANY FARTHER THROUGH THE ALT. I WAS ABSORBED TRYING TO COMPLY WITH THE RAPID SUCCESSION OF CLRNCS BEING ISSUED WHILE UPDATING THE FMS AND HDG AND ALT BUGS; AS WELL AS A FREQ CHANGE. CLRLY; I WAS TASK-SATURATED AND UNABLE TO BACK UP MY FO WITH ALT AWARENESS (I THINK HE PROBABLY SENSED THAT; AND THAT IS WHY HE WAS TRYING TO HELP ME). ALTOGETHER; IT ADDED UP TO A VERY STRESSFUL LGA DEP. IT'S INTERESTING TO NOTE THAT SOME YRS AGO WE HAD A VERY SIMILAR SCENARIO IN THE SIMULATOR (THE DEP ARPT WAS LGA) DURING RECURRENT TRAINING. THE IDEA WAS TO OVERLOAD US TO THE POINT WHERE WE WOULD DEVIATE FROM OUR CLRNC. I DON'T THINK THAT IT WAS A COINCIDENCE THAT THEY CHOSE LGA FOR THIS SCENARIO. CONTRIBUTING FACTORS INCLUDE THE ACCUMULATED STRESS FROM THE WHOLE RERTE AND ROLLING TKOF SITUATION. WE HAVE A FLT CREW AT OUR BASE THAT IS BEING PURSUED BY THE FAA (CERTIFICATE ACTION) FOR TAKING OFF AFTER A RERTE WITHOUT CHKING WITH DISPATCH FIRST FOR ADEQUATE FUEL (THE EXACT SAME ISSUE). EVEN THOUGH I WAS CERTAIN WE HAD ENOUGH FUEL FOR THE RERTE; WE DID NOT DESIRE TO REPEAT THE SAME MISTAKE. ALSO CONTRIBUTING WAS THE FACT THAT IT WAS THE FIRST LEG OF THE TRIP; AS WELL AS THE FACT THAT WE HAD EACH GOTTEN UP EARLY FOR THE DRIVE FROM OUR RESPECTIVE HOMES TO THE ARPT (FATIGUE).