Sounds like you're doing some good things but clip charts, IMO, add an extra power struggle because not only does the kid get to refuse to sit down/be quiet/whatever, they can also argue with you about the clip itself. I also don't like the public nature of a clip chart- I find they rely partly on shame which is always counterproductive.
I've never used a behaviour management system that was fiddly like that. I prefer immediate logical consequences. e.g. kiddo won't listen to instructions during art? I take his paintbrush away. Kiddo won't stop poking his friend? Now his friend will come and sit next to someone who won't bother him that way. Kiddo is choosing not to join us on the rug? Well I'm reading this story in a whisper quiet voice. He won't be able to hear it, and you better believe I've chosen a story that will get everyone else giggling.
Some other tips that have helped me with tricky classes are:
*Proximity, as one PP mentioned. You can stop a lot of annoying behaviour simply by moving in close while you continue teaching.
*Getting quieter instead of louder. I don't know why this works, but it does.
*Getting kids where you want them to be by using a "hook". Instead of instructing the class to come to the rug (and giving them an opportunity to be defiant) hook them in with a song, a rhyme, a game, or a cool video clip (space ship taking off, spider spinning a web, virtual roller coaster- anything you can then tie in to your lesson).
*Getting them outside as often as possible. I take my class out for nature walks and I teach outdoors as often as possible. We practice number and letter formation with chalk on the cement, we take clipboards and pencils and write about what we see, we even do worksheets outdoors some times. Occasionally I just take them out to run a lap of the oval and burn off some wiggles.
*Having a "calm tent". I have a small tent equipped with sensory timers, sequin pillows, sand timers and small weighted blankets. I try to catch students before I know they are likely to cause a problem and ask if they want a minute in the calm tent. Most kids LOVE the tent so hardly ever say no. This also gives me a break from that kid

*Lots of positive relationship building. I like using the Love and Logic technique of "noticing". (google it) Actually, Teaching with Love and Logic could be worth a read. I found it super helpful!
*Social stories! Explicitly teaching social and emotional skills makes a huge difference for some kids, especially kids on the spectrum.
*And yes, I do take recess play sometimes. Not often! But sometimes I think it is the only consequence that makes sense, particularly if a student has refused to do work- having to finish their work at recess a few times usually nips that behaviour in the bud. You do have to be careful with this one though because kids really need to move! If I've had to take recess play from someone, I never take away their whole play time and I make sure I build in lots of opportunities for them to move later in the day.
I hope something I've said helps!