I am grateful that Koji isn't temperamental about leads getting stuck in his hair, I just feel bad as I'm trying to get the hair out while everyone is waiting on me as I'm on the line.

Don't like that at all.
I can see Ember just giving you a pout after her hair gets stuck. Saying to you, "nope, not running, you pulled my hair out". LOL. I have seen people with the fleece or furry lined ones. Never thought about those.
As for the size, I'm not sure how they determine that. I mean, in order not to slip off Koji's head, most of the martingale's I tried, had to be really tight going on. It's like the slip part wasn't enough or something. Hope you find one that Diva can't pull out of. Fortunately for me, Koji doesn't tend to pull backwards, so it's not like he can get out, but I just work he'll figure it out.
BTW, my friend just made some clip martingales. So, you can use it as a martingale, but it just clips off for fast release. I'll probably get on of those later when Koji stops choking himself. Is this something that would work better for Ember (see attached)?