Don't wait to apply for an EHCNA, apply now. If the tutor isn't experienced in teaching primary pupils the provision isn't suitable. Ask the LA to change the tutor, although you would have to weigh up the distress of changing teacher with the benefits.
If you do pay privately, an indirect type of therapy (e.g. play, art, Lego, equine therapy) may be best. That way there is a focus on doing something rather than solely talking.
Nightimes are particularly difficult for DS1. Some of the things we have tried are various lighting, dream pad pillow, ear plugs, a 2 way monitor, brushing, worry book, tents, doodle book/pillowcase, music, white noise, various apps, weighted blanket, audiobooks, teddy, relaxation, an adapted version of gradual retreat, medication. Going against sleep hygiene advice I tried letting him watch a film in bed, and even considered bribery but decided if he thought he had failed it could do more harm.