It would look really really bad to a tribunal to put him in an indi school, having failed to provide an education in years, get him settled and then remove him at whim without somewhere else for him to go.
They might threaten to stop paying but they won't go through with it if they don't have another school willing to take him. If they do threaten it ask them to put it in writing with reasons so you can take advice on judicially reviewing that decision.
I would just let it play out. It would be really embarrassing for LA to put this in front of a tribunal. I don't think they will want to go there.
If they bring up cost just say current school must be an appropriate use of resources given there is no cheaper alternative.
They have a legal obligation to provide a full-time education suitable to his age, ability and SEN and to make provision that meets parts 2 and 3. This is an absolute statutory requirement not a best endeavour duty.
See here There is no best endeavours defence in the legislation...it is the duty of the LEA to implement (the Statement)
This is different than say social care where councils are allowed to take resources into account in deciding what provision to make. In SEN the law prevents them from using a lack of resources as an excuse not to provide an appropriate education (I'm sure there is another legal case that says that but can't find it)