Preventing idea from being stolen?

Apologies for the long post but I’m trying to be as in depth as possible.
TLDR up front is: I have an idea I don’t want my boss to steal as their own. Debating if I should go above their head or not and mention the idea to their boss so I can be the one to present it.

My background:
Former buy side analyst. Built 200-300 decks / pitch books over course of 3 years. Switched to corporate strategy / development about a year ago.

Background on current working situation:
elatively new in this role (>1 year) and have had several of my decks presented to C level and externally. From my previous buyside experience I know that usually I’m given a task and then my deck is presented by the MD or fund partner. t has been the same in this role as well, and I receive credit from the people in charge of my team for my work. The credit I receive is usually only from the VP level down and the C suite was surprised to find out that I had worked on certain projects (didn’t tell them I built every single model and the entire deck).
My specific issue:
My supervisor is a straight shooter however the department head is the one who has pitched all of my decks. Usual quid pro quo is that they get the credit and thanks while the execs are unaware of my involvement. That is totally fine because they were not my ideas. I have however brought up my own idea, that can reduce overhead and increase profitability. My supervisor and department head both gave the project a green light. However this idea of mine is one that will make headlines (well known firm, has potential to increase market share). If the idea is implemented, it has the potential to boost whoever came up with the idea’s career significantly. I’ve seen people promoted for less significant results. This one has the potential to move a senior analyst to director level or director to VP level and VP to get tapped for a C suite role.

Yes the idea is that good:
I’ve built out models with multiple cases and assumptions, and cross examined 50+ businesses globally who implemented a similar idea and results for all of them have made the news, boosted profitability, and cut costs (confirmed for publicly traded ones).

What I’m struggling with:
The project idea has been green lit by the higher ups in my department. I want to be the one pitching this deck to the C suite ( Presented externally multiple times at previous roles, internally up to SVP level in current role). I don’t want my department head claiming credit for this project and using it to get a promotion or recognition for an idea I came up with on my own and followed through with. The CEO knows me by name and is friendly. I want to present my idea to him directly and have him formally approve it. I have enough information to give him cost estimates, implementation timelines, and other key info. I just want to tell him I came up with this idea, my department also liked it, and I’d like to set up a time to present an in depth analysis when the work is completed. I’ve always been a firm believer in the chain of command and that you shouldn’t go over your bosses head unless it’s incredibly important.

What I’m afraid of: I don’t want to be seen going over my bosses head. I want to phrase it in a way where I’m asking them (the CEO) for advice and their opinion on areas I should focus in on for this undertaking. This is an incredible gamble of either career suicide or jump starts my career. I can’t ask the department head if we (as a department) can tell the CEO because then they will meet with the CEO directly and present it as their own idea. One of the C level execs and I have a pretty close relationship, should I voice my concern with them?

Does anyone have any advice? Have you ever gone over your bosses head?