The Ratchet Rule
To deal with overly negative feedback on my team, I promoted the "ratchet rule" exactly because I was sick and tired of people being "Negative Nancy" all the time. In particular, I once had a very toxic coworker that would start virtually every interaction with: "No, that's wrong!" even though he was wrong well more than half the time.
The Ratchet Rule is simple: don't accept "no" as an answer. Just tell Interrupting Isaac: "Ok, you think that doesn't work. Do you have a better solution, then?" That is, always challenge the challenger to make it better, instead of knocking it down. But apply this rule evenly to every single person you interact with. Knocking down an idea is easy, it's trivial, and the cost is low even if you are wrong. So there is a perverse incentive to puff oneself up by going around knocking everyone's ideas. Combine that with a personality pathology, and you can easily get very toxic workers this way.
You can also say: "I'm looking for solutions, not criticism." That's a more aggressive way of saying: "'No' isn't good enough." Now, Interrupting Isaac will probably be flummoxed the first time you do this, and there are two obvious reactions: 1) he will get angry that you have challenged his authority, but won't actually have a better, affirmative solution; if he's smart, he will realize that you can play this game all day long, and back off.
2) He will pause, realize you are right, and attempt to offer a better solution. This is good. If he actually does offer a better solution, then take it. Suck it up. His problem is delivery and interpersonal skills, not that he's being a jerk and wasting everyone's time. But if he just offers a different solution, that isn't obviously better, he has stepped on a land mine, because you can then challenge that by turning to your original coworker from whom you were soliciting advice and ask: "Oh, that's interesting. What do you think about that idea, Original Oscar?" This undermines the authority of Interrupting Isaac and puts him in the position of being scrutinized and evaluated, which should hopefully help him see how he comes across to others (although, he may still need guidance on processing this).
Now, if it turns out that Interrupting Isaac actually does offer useful feedback, but with poor delivery, you should ask to have a one-on-one with his boss. Just say, as politely as you can, that Interrupting Isaac offers what are often helpful suggestions, but they are unsolicited and disruptive and hurting your morale (it's also helpful if you know whether others have similar experiences with him--you say that you see him doing the same to others, but don't say how they perceive it).
Make it clear that you value his useful advice, but that you would prefer it to be offered on an opt-in rather than opt-out basis. That is, you think he would benefit from some coaching in the direction of being a passive resource that people go to for help, rather than an active resource that robs coworkers of learning opportunities and even low-risk opportunities to fail. If you frame the feedback as: "This guy needs to give us space to learn" rather than: "Get this jerk out of my face", the PHB should hopefully get the message that her rockstar is more useful as a mentor than a solve-everyone's-problems guy, and that the PHB herself can also exercise managerial skills by coaching Interrupting Isaac on how to be a good mentor.
If PHB still isn't getting it, then you need to go into more detail like thus: your team can only skill up if they act with agency and are allowed to make mistakes. Senior members can help the team by teaching instead of telling. And teaching means that Interrupting Isaac asks probing questions that stimulate further thought among the team rather than jumping them straight to the answer. That is, Isaac needs to show how he knows, rather than what he knows. With a few well-posed questions, he should be able to get the rest of the team to arrive at the same conclusions without directly revealing the answers. This requires more time and effort on Interrupting Isaac's part, but is a valuable investment in the whole team. If he pulls it off, he can go from being a resented resource to someone who is actively sought out for his insight. Be clear that you would be happy to seek out his advice if he could frame it as a teaching moment where everyone learns to fish, rather than having a fish shoved down your throat with a gruff: "You're welcome."