This is what I had in mind too!

At a business roughly the size of the one OP is talking about, we shared the password with a small group of people and kept a hardware two factor authentication device locked behind a door accessible only to a different small group of people. The basic idea is that you'd need both someone with the password (usually technical leads) and someone with access to a secret spot in the office (generally someone in finance/accounting) to log in, and locking anyone out of the office would instantly ensure they had no access.

I don't think a solution like this works directly for the specific situation that OP describes, but I do think it's a good solution for an AWS root account at an organization of the size he is talking about.

I think the answer above still stands.

Put it in a shared vault which can be accessed by however many people require it. They access the shared vault via their own password manager account.

With advanced/power user AWS IAM roles, it's feasible to eliminate it for day to day uses, meaning that you can have it so only one or two people you trust actually have access to the root creds, and everyone else can go about their business.

Shamir's Secret Sharing software, ssss, will let you encrypt a file and split it into pieces so that 3 of 5 people are needed to decrypt.

http://point-at-infinity.org/ssss/