I’ve been advised by my solicitor that if I do just take him to school the courts may not trust me to stick to any further rules/orders they put in place.
Do you have this in writing?
TBH at this point if it was me - I'd be sending one e-mail to both LA, both schools (likely won't be there till few days before terms starts), Cafcass and my solicitor - all CC in- stating clearly what the issue is two school places - also stating you put in a dispute for CB and are waiting to hear back - that you have child slightly more than 50% of time and GP and denstist are registered with you and that your understanding was you were both initally happy with this school. Be clear and factual.
State that you believe (or quote in in writing ) that this is the legal case if no court date occurs before school term date.
Ask what happens to each place - will he lose both if he starts nether on first day.
What happens if you start him at one school - and if your ex tries to take him to other school week later. If he's over 5 - and he's not attending on ex week or vice verse will attendance fines kick in.
Asking what happens if he starts late - how late - how is that in his best interests. What happens if court says he need to go to one school but the place is gone?
Asking what they understand the position to be - if they ring you rather than e-mail back stating what your understanding of the phone call was - and if their differs to e-mail you there understanding.
If the advice differs - e-mail everyone again and point it out - that they are telling you different things.
I'd want in it writing from everyone involved what risk is in taking him first day and risk of not.
It may be you can't take him in his first school day at your prefered school - but I'd want to know what that meant for the school places - rather than guessing or relying on internet posters.