Reward shop is lovely but I suspect a bit advanced for a 3.5 year old. We did a token economy with DS1 at around 5 or 6 with great success! At 3 in terms of rewards what worked was keeping it absolutely simple - he could earn "stars" for good behaviour, and when he had five, he could get a magazine. It stopped him pestering me for magazines every time we went to a shop, the stars weren't for any one specific behaviour but I'd sort of rig it so that he would end up with five about once every 1-2 weeks. I'd award one when I noticed him do something I was trying to encourage or that I knew he struggled with, sometimes I'd use them as motivation (e.g. help me carry the shopping home and you can have a star), sometimes he'd ask me if he could have a star for something he thought he'd done well and I'd usually say yes if he wasn't taking the P :)
And yes I am aware of extrinsic vs intrinsic motivation, but if you have a child who is often getting negative feedback for whatever reason, it is SO important to remind yourself to keep up the positive. If that ends up being extrinsic, so be it. I don't think it is an issue unless you are using it constantly for every little thing (which most people aren't).
I don't think there is much sense in worrying about diagnostics or neurodiversity type issues. At his age it's extremely unlikely anything would be diagnosed anyway, because there is so much overlap between ordinary, age-appropriate toddler behaviour which is the result in a not-yet-developed skill, and a slower than usual development of a skill which is related to some kind of disorder. You can really only separate it out when they are older, and really it doesn't make a difference right now anyway, because it wouldn't change any way that you should approach this. So I would not spend a long time focusing on lists of ASD or ADHD or this or that symptoms, especially of children who are younger than diagnostic age. When he's five or six, if you and he are still struggling, particularly once he's had about 6-12 months (or more) to get used to school, bring it up with the class teacher and potentially speak to SENCO, but right now the most important thing is to look at the child you have, the skills you feel he is lacking and work with that. If you feel that he does not behave because he can't, then go with that instinct, don't do something you instinctively feel is wrong just because "everyone" says well you must not be firm enough or you are letting him run rings around you.
I am not so sure about the idea to try "mainstream parenting ideas" for a month and see how you go. OK, it's a fair suggestion, if you don't feel you've implemented something consistently and you want to give it a go. Mainstream is mainstream because it works for the majority, after all. And absolutely if that's the case, crack out the 123 Magic or Supernanny and give it a proper go. But my guess/intuition from your post is that you've tried the mainstream things and they don't seem to be working, so you are now looking to well - could it be something else? It is natural to wonder, but if you could have a crystal ball and look at him in 10 years' time and be able to know whether he has this or that, would it actually be of any use to you now? Not really, because there is no such advice as ASD parenting for toddlers, because toddlers are generally not diagnosed with ASD. I suppose it allows you to have that understanding and cameraderie with other ASD parents - BTW, if you do want this, you would not be unwelcome on the SN Parenting boards here on MN, they are just out of active because it's easier that way, but you can opt-in if you go into Preferences, or navigate to them directly from the topic list. But what is useful to know is that the skills-based parenting and the non-coercive types of parenting like RIE and many (but not all) aspects of things like Attachment Parenting are all "friendly" towards neurodiverse children as well as neurotypical children. That is why it is a useful approach to look at.