Best of luck with your renewed search. As far as Bristol records go, they are thin on the ground online and it is always best to go to Bristol and research in the Record Office. The staff there are extremely helpful. If you identify records and cannot make the trip, they will often copy them and send them on, although it does cost. I spoke last year to a member of staff regarding the registers and if they were likely to appear online any time in the near future, and it seems there was a project mooted in conjunction with the LDS but that seems to have stalled. The Bristol & Avon FHS were going to attempt further transcriptions (the CDs I mentioned only cover 1754-1837 and are quite expensive) but that has lapsed owing to lack of funding. I can always check anything for you on my CDs, but of course all you get is the bare transcription - no witnesses at marriages for instance. I have several lines in Bristol (as you may have guessed from my user name I'm originally from there) and I try at least once a year to make the trip and spend as long as possible in the RO, having prepared a list of things to do.
I do have a copy of the transcriptions of the Burgess Books for Bristol, and there is an intriguing entry there, dated 13 June 1826. It records the admission to the rank of Burgess (i.e.. a Freeman of Bristol, having the right to vote etc.) of John Brown, mariner, after apprenticeship to Richard Shaw. If you get to Bristol it may be worth checking the apprenticeship records for 1817/9 to see if it gives any more information - usually a father of the apprentice is named at least.
And bingo! After my comments above I checked the Poll Books on Ancestry and in the 1830 election there is a John Brown, mariner living in Water Lane, Temple. Looks like a good fit,
Steve