"They offer 10 GCSEs rather than 9 and DS is very academic"
No. 9 GCSEs are enough, and more than many schools, so your child won't be significantly disadvantaged by it, and certainly not enough to warrant forcing the preferred school over numbers so that their student:staff ratio increases.
Most chn go on to A Level at the same school (ditto)
No. A levels are 5 years away, and many students transfer to other schools - it's very common. Ditto re numbers.
Preferred school is non-religious
No (unfortunately). Faith schools have to cater for children from non-religious backgrounds.
There is nothing exceptional in your reasons. You may be lucky - the school may put up a weak defence However, if it were possible to routinely win appeals on such run-of-the-mill grounds the school would be swamped with appeals, and crammed to the rafters.
Is the preferred school an academy or an LA-run school? You may have more chance with the latter. Sometimes, popular LA-run schools want to increase their PAN for financial reasons, but the LA won't let them because there is too much local capacity (i.e. space in less popular schools). If so, the school may put up a weak defence which goes in your favour. However, you also may find that the presenting officer is from the LA, not the school, in which case you're stuffed.
It's always a good idea to check the school's appeals stats for recent years.