Special/specialist school.
LA EPs are often not the best people to ask about whether EHCPs are watertight or not. You may be friends, but I wouldn’t rely on their advice on this. This is especially important for things like professional time, therapeutic input, equipment/tech, because they are often lacking in LA EP reports/it isn’t their remit.
Just so you know, even for online providers with accreditation, they aren’t always being named in I. Sometimes I is being left blank with the provider being part of EOTAS/EOTIS and EOTAS/EOTIS is only legally possible if you can show it is inappropriate for provision to be made in a school. I expect what goes doesn’t go in I for OEAS will be subject to challenge one way or the other at some point.
Don’t rely on the cost of transport to win your case. If the view in your particular case is it shouldn’t be named in I, then EOTAS/EOTIS won’t be won on the cost of transport if there is an otherwise appropriate school. You may have already done this, but have your search for schools included independent and non-maintained special schools up to a journey time of 1hr15?
I am not saying your case won’t be successful. I am saying you need to be prepared, know the law and target your case accordingly. For example, the LA may well revisit the ARPs and your case needs to be able to rebut that.