I seem to be late to this thread, too, sorry! I live in Cheadle Hulme and have had 3 kids who attended Cheadle Hulme High School. The radius for the kids seems to be getting narrower, so 0.6 miles is pretty borderline, so I would consider finding a house 0.5 miles away if possible. I agree that it is a big ask to find a house you like within such a narrow radius, and I had the same problem when I moved.
CHHS is the best comprehensive school in Stockport. However, they do have a lot of behavioural problems, lots of kids disrupting classes and a good number of kids who just don't want to learn. It is probably the same thing in other schools but just letting you know that my kids found that the school were struggling to clamp down on certain behaviour. CHHS had oftsed in this week so hopefully they will maintain their outstanding rating.
I have another kid who I chose not to attend CHHS if possible, and they are now at a Trafford Grammar. The competition is very intense and as an out of catchment child, it's very hard to get in although it is possible.
I agree you get more for your money in Cheadle and this is why we ruled out moving to Trafford, plus I thought Cheadle was prettier as well!
If you are really keen on sending the kids to a Grammar, I would move to Trafford and give it your best shot.
I love Cheadle Hulme. Its location is great. It's so easy to get to Manchester Airport (flight path is not over my house), good transport links and great amenities. I would really recommend it if you are happy for your kids to go CHHS.