@pasok1000, you're right that a lot of 13+ schools pre-test in Year 6 for Year 9 entry. Schools that have 11+ and 13+ entry points don't usually allow you to apply for both - you have to choose either 11+ or 13+ at the time of entry.
The usual advice is to try for several schools, even if you have a favourite in mind, to increase the chances of gaining a place somewhere. It is also advisab;e to aim at schools across a range of academic levels: for example, one "aspirational" school that would be a stretch to get into, a couple of schools that you think are the the right sort of level academically, and a "back-up" school as a safety net.
The good news is that choristers are usually looked on very favourably by senior schools, and even if your DS is not offered a 13+ place from a pre-test, it is often possible to approach schools after the main entry round and gain a place via a music scholarship. My DS is a cathedral chorister and every year some of the boys don't secure a senior school place until the spring term of Year 8 - but everyone gets a place somewhere at a school they are happy at, usualy with a music scholarship or exhibition.
With regard to moving schools at the end of Year 6, I would check the terms of the contract you have with your school very carefully. You may find that if you withdraw your DS from the school before the end of Year 8, you are then required to reimburse the school for any financial support for school or boarding fees (bursary or choral scholarship) that you have received during his time in the choir. Choir schools invest a lot of time and effort in training choristers and they don't want to lose boys before they reach the peak of their abilities as trebles in Years 7 and 8 (both in terms of technical ability and the volume they can generate - Y7 and Y8 make most of the sound). While it is true that some boys' voices change before the end of Year 8, plenty don't and it can be very hard to predict who will last the distance and who won't.
If you haven't already done so, I would strongly advise having a conversation about senior schools with the head of your DS's current school and talking through the options. Are there particular senior schools that choristers from your school tend to move on to? If you're thinking of a school that only does 11+ entry, it doesn't sound like it would be a typical destination for boys from your choir.