A message signature means I got you to do something like tap a Yubikey and enter a PIN, touch a fingerprint sensor, etc. That can still be socially engineered, of course, but it can’t happen by accident and you could add some safeguards against routine by having a dedicated “major transactions” key used only for that purpose to add a physical speed bump.
The problem is that “ignore my gmail, I list my phone” will defeat that training more often than we’d like, so you really need to have process safeguards which make it a requirement and management backing to say even the CEO will follow the lost device process rather than asking someone to bypass process, and that has to be so carefully enshrined that nobody questions whether their job is on the line if they tell the real CFO that they can’t bypass the process.
