There should be a phase transfer review meeting in the autumn term of Y6. Prior to the meeting, updated advice and information should be circulated at least 2 weeks beforehand. Make sure this happens.
In preparation for the AR, start gathering evidence to support the placement and also to demonstrate state MS can’t meet needs. For example, having concrete up to date evidence for (quantified) small class size will be a huge piece of supportive evidence. A state MS won’t be able to provide that if the wording is watertight. When you consider DS’s needs, the provision he requires and the independent MS and state MS, there may be other points along the same line. Making sure you have professional evidence for each point will help.
As well as showing state MS can’t meet needs, I would be preparing to show state SS can’t. Sometimes state SS can be cheaper than independent MS with support, so being able to showing state SS isn’t viable will also be wise. Similarly, if there are other independent MS that a cheaper who may offer a place, you need to look carefully at why they aren’t suitable.
Be aware, in order for the independent MS to be named, you will need an offer of a place. Unfortunately, just because they say they can meet need now, doesn’t mean they will definitely agree to being named when the time comes.