As suggested above, you seem to be looking at a number of different people here with the same name.
On the face of it, the will you have found does not look like the will of a married man with a wife/family, since everything is bequeathed to his fellow-seaman William Pucknell.
The captain's log in ADM 51 may report his death, as you suggest, but it is very unlikely to tell you anything about the man's origins, abode or next of kin.
The ship's musters in ADM 37 may give you his place of birth, which may or may not have been correctly recorded. There is no provision in these records for listing place of abode or next of kin. The muster for Samarang covering his date of his death in 1831 is ADM 37/7743 (1830 Nov - 1831 June). It would probably be wise to check a few preceding musters too. (Crew agreements, by the way, are a feature of the merchant service, not of the Royal Navy.)
When trying to identify RN seamen at this period it can also be helpful to look at the allotment registers in ADM 27. These give details of any pay allotted to dependants back home. They may provide the name and parish of abode of a wife/mother. Most allotment registers have now been indexed on Discovery, but (after only a brief search) John Davis does not seem to be showing in the allotments for Samarang at this period.
ADDED - from the will, the other ships on which he had served are Blonde, Iphigenia and Hyperion.