It all depends on how many weeks after application you are.... I assume you are at about 12-14 weeks and have had an Agree to Assess decision some time ago?
In our assessment all reports were supposed to be in to the LA before week 12 to avoid delaying the statutory deadlines. So if you've missed that, it is probably down to the goodwill of your LA (or how persuasive you can be) on getting the private reports included....
If I were you I would forward the reports you have ASAP and see what they say. If they say too late, try picking out 2 or 3 of the essential points you don't think you can live without and asking if they could possibly include them in the most charming way you can!
If they say no, you are probably forced to bite your tongue, smile sweetly and get the plan finalised without delay based on the LA reports - then Appeal using the new reports as the basis of your appeal.
I know that sounds rubbish but the LA can't be held responsible for not including reports they didn't get or get on time :(
I had a meeting with my LA at about 14 weeks for "co-production" which was my chance to look through a pre-Draft to make sure that it broadly covered all the things I expected. I think this is used in our LA to help make sure that no surprises appear in the 15 days after the legal Draft EHCP is issued for comment. It was only with our case officer from the LA though so was very straightforward and not intimidating at all. They then went on to issue the formal Draft EHCP straight after. (IPSEA were terribly gloomy about the pre-meeting as some LAs use it as an excuse to drag out the process but it was not our experience at all).
I hope you manage to persuade them to include all the things you want - good luck with your charm offensive!