I think I like this idea that the rotation interval could be made proportional to length, for example doubling the interval with each additional character. Security standards already now acknowledge that forced yearly rotation is a net decrease in security, so this would incentivize users to pick the longest password for which they would tolerate the rotation interval. Is yearly rotation too annoying for you? For merely the effort of going from 12 -> 14 characters, you could make it 4 years instead, or 8 years, 16, and so on.
Can confirm when I found out I'd be required to regularly change my password the security of it went down significantly. At my current job when I was a new employee I generated a secure random password and spent a week memorizing it. 6 months later when I found out I was required to change it, I reverted to a variation of the password I used to use for everything years ago with some extra characters at the end that I'll be rotating with each forced change...
I do the same but write the number at the end of the password on the laptop in sharpie. I work from home so I've been thinking about making a usb stick that simulates a keyboard with a button to enter the password.
Why not make use of a password manager?
You can’t open the password manager until your computer is unlocked.
You can put the password manager on your phone or another device.
Unfortunately, lots of end users refuse to read the password policy and won't understand why their password reset interval is "random" or shorter than their colleague's.