As you are moving outside normal admissions rounds, it will not so much be a matter of choosing a school for him (unless you pay), but finding one which has a space at the time you want it (even if an occasional place does come up, you will need to take it up within a couple of weeks of it being offered). It is worth being realistic about this at this point - I have limited knowledge of Bristol in particular, but there are many areas where all schools are full for your DS's age group and so it becomes a matter of where an occasional place comes up or where you have the best chance of an appeal succeeding.
However, on the other hand, catchments don't need to worry you, because if a school has a vacancy (and no waiting list), where you live will not matter. If, on the other hand, you set your heart on a specific school, it is currently full and it has distance as one of its admission criteria, then you may choose to find a place to live absolutely on its doorstep to put yourself top of the waiting list.
Ideally, unless you identify a perfect under-subscribed school, you would want to find an area where there are a reasonable number of schools that you would be happy with - and none that you definitely want to avoid - and apply to them all, and see where a place comes up first.
You will also need to decide on an overall strategy if you cannot find a 'good' placement initially. Will you Home Ed, send private, accept whatever school is given (which may not be the one you would choose, and may be a significant distance away) and wait to move?
Good luck! We did an in-year move when DS / DD were at primary and it was deeply stressful and had to be planned with military precision - even though DS was in a much lower birth year than the current 7 year olds so places were relatively plentiful.