HDG TRACK DEV ON DEP PROC WHEN THE CREW IS DISTR BY A LAST MIN ALT CHANGE DEPARTING RWY 33L AT BOS; MA.

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TKOF AND INITIAL DEP NORMAL. PRIOR TO 2 DME; CHKED IN WITH DEP CTL; 'CLBING 1800 FT FOR 5000 FT.' SID TURN REQUIRED AT 2 DME TO 315 DEGS. ATC RESPONDED; 'MAINTAIN 3000 FT.' BOTH COPLT AND I EXCLAIMED AND STARTED TO PITCH OVER TO KEEP FROM BUSTING 3000 FT AND SET NEW ALT IN THE MCP. ATC THEN CAME BACK AFTER I QUERIED THEM ON THE 3000 FT CLRNC WITH A CORRECTED CLRNC ALT OF 6000 FT. THE FO THEN SMOOTHLY TRANSITIONED FROM LEVELING OFF BACK TO CLB -- BOTH OF US RELIEVED WE DIDN'T BUST THE ALT. A FEW MINS LATER; ATC REQUESTED HDG 040 DEGS AND THEN WE REMEMBERED WE NEVER MADE THE 2 DME HDG CHANGE TO 315 DEGS. DUE TO THE MULTIPLE ALT CLRNCS GIVEN AT THE 2 DME (WHICH REQUIRED IMMEDIATE REACTION OF BOTH PLTS) THE TURN AT 2 DME WAS MISSED. SUPPLEMENTAL INFO FROM ACN 539376: WHEN THE WT AND DATA ARRIVED FROM THE GATE AGENT WE FOUND WE COULDN'T USE RWY 27; WHICH MEANT WE HAD TO CHANGE THE DEP. WE WERE ASSIGNED THE LOGAN 2 DEP AND RWY 33L. CHANGED THE FMS AND REBRIEFED THE DEP. THERE WAS A CONSIDERABLE DEP DELAY DUE TO POOR WX AND HVY TFC. WE HAD TO WATCH OUR MINIMUM FUEL FOR TKOF; SO WE TAXIED OUT ON 1 ENG. STARTED THE SECOND ENG IN PLENTY OF TIME BUT THE TKOF CLRNC WAS A BIT OF A SURPRISE AND THE BEFORE TKOF CHKLIST (WHICH INCLUDES A PRETKOF BRIEF ON HDGS; ALTS; AND AIRSPD RESTRS) WAS RUSHED; IE; I SAID THE WORDS; BUT DIDN'T THINK ABOUT IT CAREFULLY. THE PNF DURING THIS WHOLE TIME IS CHANGING FLAP SETTINGS; MCP PANEL SETTING; RADIOS; ETC. PRETTY BUSY. BIGGEST REASON FOR THE DEV WAS THE DISTR OF A LOW ALT HOLD DOWN DURING A VERY BUSY PHASE OF FLT. WAS A BIT RUSHED ON PRETKOF WHICH DIDN'T ALLOW A THOROUGH REVIEW OF THE DEP; AFTER A LONG SIT WAITING TO TAKE OFF. PROBABLY NEED TO SLOW DOWN. OVERALL; YES WE MESSED UP; BUT WE FELL INTO A TRAP.