Help everyone in your organization use a good password manager. (I should disclose that I work for the makers of a very fine password manager.)
Seriously, you have a password management problem, and using a password manager within your organization is the best shot at addressing it. This is what password managers are designed to deal with.
There have been a number of excellent comments my rather off-hand answer. So it looks like I'm going to have to put in some real effort here.
There are two questions to discuss.
Forgetting the password manager password
A password manager does not eliminate the need to remember all passwords, but certainly does help. It wasn't entirely clear to me whether the original question was focused specifically on the workstation/AD/LDAP user password for the organization or other passwords as well.
One thing about using password manager is that you typically need to type it its password several times a day. So after a short while, people do learn it well.
And talking specifically of 1Password, we have things set up so that it is impossible for us learn anyone's secrets, but it is possible for certain individuals within an organization to be empowered to perform recovery. See either our documentation for what this looks like to an administrator or our security white paper for the gory details of how that all works behind the scenes.
Of course you can't run your password manager on a system that you can't log into. But depending on your organizations policies, the password manager can also run on a user's phone.
I understand that there will be some objections to this, but consider that it is in the organizations' interest that people's sign on password not be something that they also use for the HTTP only
MyKittyPictures.org which is built on a version of Wordpress that hasn't been updated in a decade. So you do want your people use a password manager at home as well as at work.
Again, 1Password (and some of our competition) allows ways of managing separate accounts, so that you don't find workplace secrets leaking into places you don't want it to. I didn't really want to turn this into a sales pitch, but there are ways to set things up that work for the security needs of various organizations.
With unique passwords, the need for forced rotation diminishes
(This is relevant because forced password rotation leads to people forgetting passwords or using crappy ones.)
Forced password rotations generally do more harm than good. Some of the "good" that they do is because people tend to reuse the same password on multiple services, and so once one gets compromised the everything using that same password is vulnerable.
Getting people to use a password manager helps move people away from password reuse.
With generated passwords, complexity rules aren't needed.
Password complexity rules may also do more harm then good, and they certainly lead to passwords that are hard to remember. 1Password nudges people toward very strong, but usable, master passwords.
Again, I'm not trying to turn this into a sales pitch. Look at what we offer (talk to us about your specific organization's needs), but look at others as well. We are the best, in my not so humble opinion, but my over all point is that many of your password problems can be addressed through the use of a password manager. And it will get your people engaging in more secure habits. A password manager enjoys the happy spot of both increasing security and making life easer for users.