I'm not going through this now but have done in the past. DS1 is 8 and was diagnosed when he was 5.5 and the process started when he was 3.5yrs.
It does take a very long time but in some ways that is good as they do change a lot at that age as you have seen for yourself.
My DS ended up with a dx of Aspergers, although it is very mild. He also has dyspraxia. Apart from the speech delay, he sounds a lot like your DS. He is also very affectionate, preferred adult company to other children, can talk for hours on his favourite topics. Not great at conversation unless it is question and answers. Not great at 'sharing' a conversation - it has to be on his terms iyswim.
My advice, although a bit lame, is to try not to worry about it. What will be will be. If the paed says he is probably mild then it isn't so bad. He will find his place in the world. Make a note of the things he finds difficult, what he finds easy and anything you think you are worried about. The assessment will rely as much on your thoughts on him as anything else - there is only so much they can pick up in an hour or two of tests.
He has been picked up early and he will be able to start school with them knowing that there are problems and if it is a decent school, they will be able to make allowances for him and help him.
I also found that when the diagnosis came, after 18 months plus, it was a bit of an anti-climax. We all knew what was coming. I know not everybody feels the same - some people find the dx a shock even though they know what is coming. However, from my point of view, where you are at now, just at the beginning, wondering what is really happening with DS, was the hardest bit. I hope it is the same for you because it means that it can only get easier.
Anyway, welcome. Don't be afraid to ask any questions you want. There is bound to be somebody who has already been through what you are going through no matter what it is that is bothering you.
Just bear in mind it can be very addictive!!!!