I am going to apologise in advance, but this will be long!
I am also going to leap in and say not to over pathologise the lack of narrative recounts of the school day. I am a highly verbal NT female (which doesn't apply to a lot of your kids) and I hated this when I was a child and still sometimes feel irritated if I am asked about my day (although I comply with a "it was alright" or "nothing special" or "not much happened" as I know this is polite). It is developmentally normal for children to troubleshoot the bad bits and leave the good bits out, though of course it is a thornier issue when you are dealing with anxious children who really do need to talk about something but choose not to because of their anxiety so worth pursuing if there are issues...
It may not be relevant to all, but is also the case that as children get older they may not tell you as you are their parent. It was ever thus with all older children and teenagers.. I have a student (secondary of course) with ASD who apparently never verbalises thoughts or feelings at home. Today, he and two peers had a very lengthy conversation about the value of logic in understanding NT interactions and how frustrating it was that NT people were so unpredictable (Aside: there was a really great moment where one of the kids said: "oh you know, X, you are just like a falcon.". "Falcon? That comment makes no sense!!", "you know, a falcon, an alien being that loves logic.... VULCAN!!!). They all laughed hysterically and agreed how much they hated "our" illogical approach to behaviour!
In terms of intervention planning, verbal responsiveness and contingent responses are key social skills in terms of conversation for students with language and communication disorders (not necessarily just ASD).
There are all sorts of ways you can work on them..
- script conversation as above, moving from immediate and familiar, highly preferred experiences to less preferred ones etc
- script conversation and demonstrate the turn taking nature of the conversation between 2 people with each having a different set of coloured cards, every time you say your "bit" you put down a card. This teaches a prompt for tracking turns/topic changes in more improvised and larger group conversations
- reduce the script once you have mastered several until you can give one word or topic prompt card, keep the coloured cues (script fading can be tailored to your child, some children need to fade out words, sentences or other prompts but this can be individual)
- Increase the number of conversational partners
- Decrease the familiarity of the situation (not at the same time as increasing other demands!)
- Get kids to focus on the good of each interaction where you can.. this is particularly crucial for students who are anxious. Sometimes, it is best to just look at successes and not focus or draw attention to things to improve in the early stages. Video modelling approaches often use this as a strategy - tape lots of scripted stuff and then edit out all the prompts so your child sees a smooth, successful interaction. You can reward them every time they watch it, as well as pairing this with verbal praise.
- Responsiveness diary/Set ups.. Create a special book, have your child decorate it with things that make it appealing to them e.g. Sponge Bob or whatever, and set up situations with familiar adults with a script then without one/less familiar adults with a script then without one/unfamiliar adults with a script then without them and then repeat hierarchy with peers, then repeat increasing number of conversational partners.. Build in rewards and levels e.g. give the child 2-3 compulsory things they must do in the situation e.g. say hello/respond to hello, ask for an item (e.g. shop) and say thanks when they get it. Have a clear reward for each to be collected after the interaction. As this is mastered, start to add optional extras e.g. say "the weather is awful today" and look at the lady, say something about the weather, ask the lady a question about a delivery etc (tailored to individual interests etc).
There is a huge amount of information on how to do lots more tricky social interaction things in the Social Thinking curriculum by Michelle Garcia Winner www.socialthinking.com e.g. building bridges between topics by working a conversation round to what you want to talk about. All our students who covered this material use this strategy spontaneously now.. There are lots of good ideas in this material which are practical and my students find them very motivating..
As I work with a group very verbally and cognitively able students with ASD, I would say that if your child meets this sort of profile it is important to build in cognitive rationales (e.g. WHY you are doing it, WHAT the purpose of it is etc) from early on. You want to match this to the language level and motivation of the child initially, but as they grow older it can be very abstract.
For much older and more able students, there is a protocol for really examining the nitty gritty of social interactions with a motivated teen (and we have lots of them in our settings who have diagnoses of both SLI and ASD) by Brinton and Fujiki.. the article is old now but the process it describes is one I have had success with, it's called "If you can have a conversation, you can have a relationship..".
Finally, the key to social and conversational success is to be successfully involved in as many social situations and conversations as possible. There are parts of these interactions that are pretty difficult for kids with ASD in terms of the underlying neurological issues that make e.g. facial expressions hard to read, multiple cues hard to process but there is huge progress to be made through learning the skills that we use to think about others and how they think about us.