New to ASD-looking for best route for assesment

Hi All ,
Quick round-up. I noticed issues with my second child-a boy-when he was around a year old. There is a big gab between him and his sister-8 years,so babies were all new to me again, as was a boy. He was placid, slept and breast fed well,very attached to me and in general a great baby.He has always been affectionate, to me espically,and has good eye contact. He met all the usual milestones, or so I believed,but I found myself making excuses at every developmental check as he would not do anything the nurse asked. Id reschedule for another day. At 2 I knew speech was very delayed and balance was off. His brother was born when he was 2.5yrs and there was regression. I reasoned that it was a reaction to the new baby but I knew it was more. He started to remove his own nappy and smear the contents. Once this happened I made an appointment with a pediatrician. She said there were ASD red flags and to be honest it didn't surprise me. I worked in the background in children's mental health services in my 20s and I could see it myself.
She recommended full HSE assessment-as he would require it for learning supports in school, speech therapy and OT. I asked about private assessment and she advised we use the money ,until hse assessed, on s/t and o/t. He was seen by her at 3 and we immediately found a fantastic o/t and commenced treatment. He is currently on his 3rd block and there has been immense improvement. He had 2 blocks of s/t but the therapist, although lovely,wasn't the right fit.
We are having difficulty finding another and would appreciate any suggestions.

He is also being seen by enable Ireland. We have had a s/t assessment and pre school visit and an o/t assessment. I am pushing very hard for a multi disciplinary assessment as is our o/t. She is doing a school assessment in 2 weeks, I am having a full medical for him and we will be sending all info to Enable to push for a full asd assessment early in the new year.
His o/t has said all along he is high functioning and complex. He possesses some very clear markers but he doesn't stand out. He has very clear sensory issues with touch. He has verbal ticks, hits himself, echolalia, sensory processing issues ,tantrums and vestibular issues. I am just wondering if you would recommend us getting the private assessment anyway? I feel like we would be able to serve him better and prepare him for school in September-he turned 4 in July. If he needed another years prep I would send him to a better supported pre school. I am trying to navigate the system, but Id go without anything to privately asses him if it was the best course. I feel it is but all the specialists I've seen so far have advised spending on intervention. Ill happily spend on both!
Really-I just want to know if its the best course and if a school will accept a private diagnosis and offer sna assistance based on that.
Apologies for the long post. As with every asd mother-my child is my priority. He is the most amazing, loving, gorgeous little human and I am blessed to have him. I just dont want to miss a single opportunity to offer him everything to help him and I never want money to be the issue he didn't get everything I could do for him. He has private insurance if that makes a difference.
Thanks for reading-any advice from seasoned parents would be much appreciated.
C