As you say, midyear it might end up being a bit of a lottery.
Amongst the Harrogate state primaries people normally just go their nearest one, with the kids typically walking to school alone from about the age of 9 [?ish?].
If you're serious about church, you might want to include St Peter's, it's in the town centre & generally thought of as 'good'.
If you're on the kind of West/SouthWest side of town, Western [traditionally very popular] and Rosset Acre would both be seen as 'good'.
Pannal would be very good if it's your nearest, or near enough nearest, school, but not so good as to e.g. justify a longer drive.
Really Harrogate is overall a very prosperous, pleasant, place, all of the primary schools are totally fine. Even the less traditionally 'des res' areas [there are a few mixed areas in, crudely, the North & I guess East sides of town] are totally fine.
I wouldn't be super eager to send my kids to say Grove Road or Starbeck, but I'm not sure there are any others that I'd put in that category. Like I said, Harrogate is in the main a really prosperous, pleasant, place.