I can't offer practical adivce on the nursery but I can help with ways to manage the transitions and waiting.
What do you have in place to help him cope with transitions?
Visual timetables are very good for kids with additional needs. You can make one yourself and there are lots of resources where you just print out the pictures and stick them in order you choose.
much like these www.sparklebox.co.uk/special-needs/visual-timetable/home-routines.html#.WFVEtOCLTnA
Obviously this means you need to keep a strict-ish routine with your DC but if it minimises the lashing it out it could help you enormously and the knock on effect would be that you could transfer it to nursery/alt childcare and that should help minimise some of the anxiety.
I used one for my DC to help with morning routines - this one was rigid and never changes - and to plan the weeks activities so nothing would be a 'surprise' we had removable cards to stick on the timetable for dentist, doctor, bus journey, shopping trip etc.
I'll be honest it is a faff, you have to be focused with it and make sure you plan and remind DC in the morning what's happening in order. I'd snap a photo every morning of it so we could take it with us. That was very helpful.
The waiting bit. Something really simple as a timer could help you out there. A big bright one that measures in minutes. A toddler can't be expected to wait for very long but using a timer to measure a minute or two at a time to practice waiting might help.
We used a timer here a lot for things like dinner if it was going to take 20 minutes I could set if for DC so DC knew when the timer goes off its dinner time and DC could see how much 'time' was left.
Big colourful egg timers might be a better bet with a toddler though. a bit like this. www.amazon.co.uk/dp/B015SDGVMY/ref=twister_B00SK5V68W
You can double this up for things like teeth brushing and use it in small games so your DC gets used to it.