"Everything works fine when I copy and paste my current password for Chase into Quicken's One Step Update Settings page. The same password is rejected by the Password Vault. 'Chase could not use the password you entered.'"
The problem is most likely that Quicken does not have the current password rules for the financial institution.
When you attempt to enter a password at Tools > Password Vault > Add or Edit Passwords, Quicken uses password rules supplied by the financial institution to verify the password: if the password you try to enter does not conform the the password rules Quicken has, the password will not be entered in the Vault.
However, when you do not have a password in the Password Vault for a financial institution and you attempt a One Step Update (or Update Now), Quicken will provide a box for you to enter the financial institution password. Once you have keyed the password, Quicken will allow you to check a box to the left of that password you just keyed, telling Quicken to "Save" the just-keyed password in the Password Vault. Quicken does not edit that password before entering it in the Password Vault.
That is a way to temporarily work-around the problem of Quicken not having current password rules for the financial institution.
Users experiencing this problem should contact Quicken Support or the Quicken liaison person at the financial institution to get the password rules updated.