This is a good way to get your ideas implemented, but your manager is always going to be able to take credit. If you are able to develop a situation with your manager where they see you as equal or near equal, they won’t mind if you bring them in on emails or meetings or whatever with their boss, so you can take the credit you are due. Extra credit if you get them to set up the call or meeting with the three of you and then you get to lay it out.
We had great health inspectors at my former food service management job. There was no way to conceal that we had mice. But the mice never touched the food. My district manager had made a room towards the back into a chill meeting room with couches from Habitat for Humanity. Those couches turned into their nests.
I went so far above and beyond to fix the mouse issue. I tore out a drop ceiling in one of our dry storage areas with no training and no protection. I was getting below minimum wage at the time because I was on the lowest possible exempt salary. I got showered in mouse shit and who knows what I breathed. I did this because the inspectors were cool and wanted to help us with the problem instead of shut us down.
They forced us to use glue traps through which I disagree with morally versus kill traps. I used oil to set many mice free. Most of them probably went back into the store.