Thoughts on the update:
Torrid: Big improvement. Simpler, seems more balanced, and fits the theme. Might want to indicate if it's max +2, max +3 or max +4 (not recommended, but could be).
You have a couple of really colourful weird moves, but only one statline has a non-negative weird, and you don't even have +1 weird (max +2) in your advancement scheme. That's . . . well, weird.
Show-off: might want to amend it to 'a bystander is watching'. You're showing off to an audience, not your opponent, after all.
The world's a stage: why can't they back off? I'd interpret it as turning tail and bailing town, but the concept's the same. While I'm not sure what to replace it with, s-harm indirectly doesn't seem that much of a deterrent. I fail to see what they lose by choosing to suck it up each time (unless they just happen to be doing something else important at the time).
Arena clown: This one is interesting, but, I dunno, seems 'off' somehow. Partly, I think it doesn't quite fit the tone of the rest (which are the moves of someone who's a show-off, but serious), and partly the 7-9s are *nasty*, at least when it's a PC who can choose which result. I'm not sure I'd describe it as a horrible move, but I can say for certain I'd never take it, so something's missing.
Special: so, it's either an orgy or nothing. Suits the concept, and will result in nothing but trouble. I like it, but +1 forward may not be enough of a carrot to incentivise the character into walk into that much trouble willingly, which would be a shame, but on the other hand, you don't want to make the move too complex.
Also, doesn't seem to be a difference between a hard and a soft hit. Maybe make a hard hit better, so as to provide the bigger carrot.
Also, you don't specify a maximum + for the roll. Is this deliberate, or do you want to specify max +3 or something. Maybe after that, they add to the intensity of the effect?
Regardless, a huge, huge improvement.
Is there a reason there's no +1 cool/sharp (max +2) - both are very useful for a combat character, and at least give the character the option of not taking 'Show Off' or 'Tactical Mind'.
Frenzy (weird) and Reputation (Cool) are strange choices to have for a character who can't improve either stat beyond their starting values (max +1). Don't get me wrong, they fit the concept, but they can't get the stats to back them up.
I think some indication of what +community should do would be helpful. The only thing I can think of would be on a 7-9 result, taking it would mean that at least the more destructive fallouts are not self-inflicted, but what would it mean on a 10+?
You have +1 overburden, but it's not mentioned elsewhere. Typo? (should just be +overburden?).
Fallout: +litter. I know this is a positive choice, but for a fallout this mild, you might as well not take it. Honestly, simply having fallout: litter is good enough on it's own, as it gives you a 'safe' fallout option on a 7-9, but that's really kind of lame. I'd either change it to fallout:thrown debris (take (1-2)-harm area) or remove the fallout option entirely and just have them throw pretties.
Do you intend for 'inability to deal' to result in mass suicides, or something, because that's how I read it. Cool if so, just want to be clear that's what you mean.
And that's it for the moment. I like a lot of the changes here, a big improvement over your first draft. Keep it up!