I would also second AReallyUsefulEngine. Spending thousands on lawyers isn't usually necessary. I have known friends have very mixed outcomes when using lawyers at tribunals. I know it can be daunting to do it yourself. Ipsea and SOS!SEN are charities that offer free advice. They really know the law.
If you are entitled to benefits, you may be entitled to legal aid for a tribunal anyway - and that firm could pay for new reports.
If you're not, the money you might spend on a lawyer will be far, far better spent on getting independent reports done. Even then, you shouldn't be looking at the kind of costs you're talking about. (Although it could be £2,000+).
You say that your DS is getting additional help anyway so you've been advised that it doesn't need to go in his EHCP. I would question that. It really should be added to Section F - otherwise it could be removed at any time. You say that your DS is moving schools. If the provision isn't in Section F, there's no guarantee that it will continue.
You say you've got an annual review meeting coming up. There is some good info here on what to expect and the timeframes the LA must stick to:
www.ipsea.org.uk/annual-review
By 'enhanced EHCP' - do you mean getting additional support written into it? If so, there needs to be evidence of what and why it's needed. That evidence will need to come from experts - eg speech and language, educational psychologist etc. You can request this at the annual review meeting.
In terms of what's achievable in an EHCP, it's really down to what evidence you can gather. I know DC who are in private boarding schools hundreds of miles from home, have all kinds of therapies (yoga, horse riding), respite care etc. Some of this has needed a tribunal to win but it can be done.