Hmmmm. Looks as if you are going to have to go for the muster roll, though I would be inclined to try the log first.
While my sample size is admittedly low, from looking through the ship's books for two voyages of East Indiamen to the Far East I would say that the Ship's Log should not be your first priority.
I found the Logs to contain mainly:
Ship's position
Weather
Other vessels encountered.
Mentions of the crew were extremely infrequent and then only in the most general terms such as
set the crew to swabbing the decks. When the ship was anchored the Log is even more terse.
My ancestor left his first voyage at St Helena in unusual circumstances - according to him, at the particular request of the Governor of St Helena and his ship's Captain (as he possessed a trade in which the Island was then utterly deficient). Going in I was sure the Log would mention this, but not a word was found.
The key source for crew information (at least in the East India Company context) is the Pay Book or Ledger of Wages. This did mention his discharge at St Helena but no more than the fact and the date. It also mentions the date of entering the ship and has various calculations regarding pay and levies/duties (things like purserage and Greenwich and Poplar Hospital Duties). Also it states position in the ship - Sea(man), Sailmaker etc.
For these ships there weren't muster rolls such as might be found for an infantry unit. There was a list of ship's company (from memory, loose leaves tucked inside the cover of the Log) which noted the man's position and those who had run or died of sickness and accident. That list, the Pay Book and the Receipt Book for wages paid at discharge were all that reliably related to the crew.
The two voyages mentioned departed in 1803 and 1817.
