the route to dx is different in different areas, unfortunately. I can only advise based on the areas I have lived in.
we did not have EP involvement at all during dx. we had (multiple, mostly pointless) visits to the community paed - wait 6 months and come back type appts.
then we were referred to social comms clinic (finally!), where dd1 was seen by paed and SALT together (a sort of mini multi-disciplinary). they had to both be present at the appt to get the agreement, otherwise the observations were not valid as dx obs (ie we went for a 2 hour appt. at the end, the paed said to the SALT "so, do you agree with what I am seeing?" and SALT agreed. all done and dusted)
my concenr for your situaiton is that you get a private EP involved, at £££ to yourself. EP observes, and writes a report. but the paed was not present at that obs, so cannot verify it, and the EP was not present at paed's appt, so cannot verify it - iyswim?
I have not heard of EP being involved in dx before. they advise schools/parents on educational matters, ime.
smug: we paid around £1800, I think. but that was for Tribunal report, with a full day assessment of dd1 at her school. he gets booked up very quickly - we have oftenhad to book him many months in advance (he spends large amounts of time overseas, so his time in this country is very full).