Ofsted reports certainly don't tell the whole story. But the fact that the three schools you have mentioned - Sea Mills, Avon and Badocks Wood - are the names that come up again and again as ones parents have been offered who can't get places in their local areas does tend to suggest that they are unpopular for a reason, if they can't fill their places with children in their own area.
A lot of the Ofsted rating seems to be based on Sats results, and unless a certain (high-ish) proportion of children are meeting national average expectations of levels, they will never be rated good or outstanding. This can be very unfair to schools in deprived areas or with many new immigrants, who could be doing amazing work with children and getting them to achieve well above what would be expected from their backgrounds. This is one reason people sometimes rave about schools rated merely satisfactory.
Things can also change - a school which has been in special measures and has had a new head, new staff, more money etc can sometimes be a very good place to send your child, as things can improve very rapidly, and it can take local perceptions and Ofsted ratings a while to catch up.
But as far as I know, none of those scenarios apply to Sea Mills etc.
Really, you need to have a look around the schools (as many as possible, even if they don't have places available immediately) and judge for yourself. Are you going to be able to make a research trip over to the UK before you actually move?
Based on your plan to live in Sneyd Park, I'd say the schools you should probably be looking at would be Stoke Bishop, Elmlea, Westbury CofE, Westbury Park, St Johns (just over the Downs near the top end of Whiteladies Road). Slightly further afield, Henleaze or Christ Church Clifton are also worth a look. And take a look at the ones the council has said have spaces, to see what you think.