Advice please: state secondaries with firm behaviour and excellent dyslexia support

The good ones. Most likely. But you can be lucky.

I work in In Year admissions and current Year 9s (so September 26 Year 10s) was probably our biggest cohort and this was the same across all the neighbouring LAs as well. I work in a city in the North West. If you had a vague idea of where you were considering moving to then you could look at last year's allocation for Year 7 to get an idea of where had spaces after the initial offer day but as your search seems to be anywhere in England then this going to be easy.
Rural doesn't mean spare places. Schools will either be in a larger town or will have taken pupils from a wide area. In the city I work the most in demand schools have a radius of under a mile at Year 7 application time. After that it's waiting for a place or winning an appeal.

If there are no spacers whatsoever for your older child then they may use the Fair Access Protocol to place her. This can be used where there is no school within a reasonable distance which can offer a place. Year 10 and 11 are my biggest problem for placement and that's due to the exceptionally large year groups. All the LA has to do is offer a place, it doesn't have to be at a school you like or requested if those schools are at PAN or over.

You can apply now if you wanted but you will be bottom of waiting lists most likely. If you're Catholic or other faith you might get a bit higher up the list compared to non faith applicants but as noted above you'd be expected to take up the place within a few weeks of it being offered, I've never seen an offer made more than 6 weeks ij advance.

I think you need to narrow down where you would live and then explore further and look properly at the logistics. Saying any city or commutable to London is basically ruling out Cumbria and anything further west that Bournemouth but leaving the rest of England. And just because a train route exits it doesn't make it easily commutable Leeds can be two hours to London but it's a pain in the arse and doesn't include the slog from home to the station. Commuting in Leeds is absolutely awful. Likewise Manchester and Leeds.

For year 7 in England any application will be treated as late now, so “choices” are likely to be limited and you will be allocated wherever there is a space after the allocations are made. At that point you can go on waiting lists.. Did you make any application for them by the October deadline? Where are you currently living? Likewise your y10 will only be offered a place wherever one is available, which may not be local or at one of your choice.

Scotland has a completely different education system @SecondaryChoicesIncRelocation . They sit Nat5s, Highers and Advanced Highers and I have no idea where Yr10 is in relation to their qualifications. On the plus side, your "catchment" school has to take you I believe (although I'm sure someone Scottish will come and correct me shortly!)

Are you currently renting or will you have a house to sell?

winchester and beaconsfield maybe oxford as well?
from what i've read all three of these areas tend to have good results. maybe someone can help with targeting specific schools.

What do you mean by good rail links? Are you looking to go into the office 5 days a week? How long a commute are you prepared to put up with? Really you need a decent area with a few schools to maximise your chances with a late application, but it’s hard to know where to suggest without some guidance!

Tbh that schools are very few and you have missed grammars. Even grammars don't fit your list.
Sorry. A lot of the good state schools are full now and service is much higher in private schools.

Look at undersubscribed schools. You can lucky, find a home and apply.

I think @gogomomo2 is mistaken in saying they won't accept your application until you are resident. I think you could apply to a Durham school from Cornwall if you wanted to. However you would apply via your own LA and as we both said be ready to take up the space quickly. Also of course if you are 400 miles away you would be lower down any waiting list!

The Hertfordshire & Essex High School in Bishop’s Stortford might be worth a look. I think it may well tick a lot of your boxes.

Honestly, you won’t get a choice, you will be applying late (for year 7 entry) and in year for year 10 so will have to take available places. They will not accept your application until you and crucially the dc are resident in the area you are applying to. I know this sounds harsh as opposed to giving you school ideas but you need to be realistic. The availability will be the schools where they are undersubscribed. Concentrate on where you want to make a home, accept the school may not be your first choice and you may need to consider private support for dyslexia and school more generally if it’s not an ideal school. I’ve done in year admissions and you also may have up to 6 weeks between application and starting so time your move carefully, you do need to applying by beginning of July for entry in September due to the holidays

Many schools will only start GCSE curriculum in y10 anyway, so forget all the matching options blocks and boards, just go for a school that starts most/all in y10.

I'm hoping you made this decision before half term and got on and applied locally for a y7 place. If not then get on and do it. It will be a late application but better than nothing.

Frankly it seems as if you think you can pick what you want. For the y10 it will be about who has spaces, and for the y7 if you haven't already applied you will be behind on time applications.

For the y10 (or current y9) you will have to take up a place with 4 weeks or so (dependent on LA) so you have to either apply soon but be prepared to move if a space comes up, or wait to apply until early June or so.

Remember the best schools will be full!

Do you have any geographic restrictions or preferences?