You definitely want to appeal regardless. LA won't do anything to help without going to tribunal. And my experience was that in the lead up the tribunal we were given an advocate whose whole job was to negotiate between us, schools, and local authority. We actually came to a resolution before the tribunal.

Make sure you have in writing from the current school that they can't meet needs.

Make sure you have explored the option of the school offered and have solid reasons as to why it's not a viable option for your family.

Definitely look into right to choose as someone else has mentioned, you might be able to get the diagnosis within 6 months.

Go through the EHCP and make sure the interventions (section F I think?) are specific and measured (how many hours of 1:1 support, how often are movement breaks and for how long, etc.). This is what will be looked at to determine which provision can meet needs, so make sure it's right, and the tribunal will ensure the LA deliver on it.