Hardholder's way too much of a stretch. You have to squint to see it. Operator's nice and tidy, with maybe a dash of the Hardholder's personality, I'd say.
Imagine the playbooks as broad strokes and not personalities. Like, Jayne's a conniving and scheming Gunlugger - just being a troublemaker doesn't make him a Battlebabe, even though that's what Battlebabes will sometimes do. The Battlebabe just lets you use that behavior as currency.
Like, Vincent will have to give you final word, but I don't think you can find their mates by drawing analogues in their personalities and antics: you have to look at the basic description.
Kaylee is a Savvyhead, because she's good at working on things - sometimes spooky good. Don't concern yourself with, say, her cheerfulness, her heart, or her undying optimism. Just that she's a techie. Your savvyhead can have any kind of personality, after all.
Wash is a Driver because he pilots the main vehicle, and because he's most competent behind the wheel, so to speak. Don't concern yourself with his knowledge, capability, or enduring love for his wife. Just that he drives.
Mal is an Operator because he commands a crew of people and takes jobs, some of which go well, some of which don't. Yeah, he runs his crew with a bit of Hard, just like a Hardholder, but that's really it. Your Operator could be a jerk, also - hard-hearted, stoic, "the crew is my family". Your Hardholder could be the exact opposite.
In that way, Jayne becomes the Gunlugger because he dishes out hardcore pain, has a lot of weapons, and is the baddest ass (no offense to Zoe and all, but I'd much rather have Jayne as security when it gets down to it - providing I can pay him enough.)