Why, and how to increase 16-character lockscreen password limit? This is a problem that has annoyed me, as the password that I have memorized is around the 20-character mark, yet Android limits it to 16 characters

Why, and how to increase, 16-character lockscreen password limit?

If it's relevant, the Android is running on 5.1 Lollipop.
From Android Security Internals: An In-Depth Guide to Android's Security :


  Android doesn’t have a dedicated setting to manage the encryption pass-
  word after the device is encrypted, and changing the screen lock password or
  PIN will also silently change the device encryption password. This is most
  probably a usability-driven decision: most users would be confused by having
  to remember and enter two different passwords at different times and would
  probably quickly forget the less frequently used, and possibly more complex,
  disk encryption password. While this design is good for usability, it effectively
  forces users to use a simple disk encryption password, because they have to
  enter it each time they unlock the device, usually dozens of times a day. No
  one wants to enter a complex password that many times, and thus most users
  opt for a simple numeric PIN (unless a device policy requires otherwise)
  
  Additionally, passwords are limited to
  16 characters (a limit that is hardwired
  in the framework and not configurable), so using a passphrase is not an
  option


(Emphasis supplied)

I don't know more about this limitation and would be glad if somebody can amplify (Edit: Andrew T has clarified here to an extent)

So, that rules out increasing password length to beyond 16 ( how to increase, Androids 16 character lockscreen password limit )

Since you are on Lollipop , you may like to related pitfall (claimed to be fixed) of long passwords here Android lockscreen can be bypassed by overloading with massive password

Note: 


For earlier versions (Lollipop and below), Cryptfs Password by Nikolay Elenkov, allows you to set a separate password for disk encryption or if your device is rooted 

su -c vdc cryptfs changepw new where new is your new  password.

Source: http://nelenkov.blogspot.be/2012/08/changing-androids-disk-encryption.html
Nikolay Elenkov is the author of the book Android Security Internals: An In-Depth Guide to Android's Security and runs a blog here