I'm in line with your take. I think that's pretty much exactly how they should handle Hangman.
The "what does AEW need" thought train is just kind of interesting of me, so I kind of spun that off in a different direction.
There's one side of me that says "I don't know that AEW needs anything". They've successfully set-up an "Upper middle class" American wrestling company, and have made a lot of big moments and regularly put on a quality show. Their ups and downs aren't anything that I consider overly problematic. I'll definitely compliment or critique in the moment, but its all...realistic.
On the other hand, as really the only other alternative on a near mainstream level, I do root for them. And their owner has pretty regularly made WWE a point of comparison and held them up as something he shoots to surpass. To get anywhere close to that in the next 10 years, there is obviously "need".
You don't get there over night, or even in a year, so its interesting to ask what would get them to the next tier in a sustainable point. The obvious answer is that plus level superstar. However, I'm not sure that's realistic for AEW. One, I'm not sure that the fandom isn't a little more segmented and maybe a little more resistant to "mainstreaming" tendencies (Unless its the women's division-but that's a separate HOT TAKE). Also, with the more New Japan style combined, it almost takes a group to interact well with most of the roster.
Where AEW differentiates is in the style and match presentation. So....what could they do different to level up that is unique to them? I've been thinking they need to capitalize a little better on some of their big moments, and educate build more on their cross-promotion and "Forbidden Door" events.
Also, extend Eddie Kingston's rehab time period.