Sometimes, you just need to brute force a fix for your macOS launchpad...
Saving this here for future reference (and in case anyone else needs this).
The *.db file was missing from com.apple.dock in ~/Library/Application\ Support/Dock. Resetting LaunchPad, killing the dock, and all the other recommended solutions did not fix the issue, so I first copied the missing LaunchPad DB file from another user on the same computer. This did not immediately fix anything, so I started to search through the Preferences and .plist files in the ~/Library directory to see if the options for ResetLaunchPad were changed. I discovered that there weren’t any keys for ResetLaunchPad or LaunchPadDBName in my com.apple.dock.plist file at all.
So I found a unique com.apple.dock.$HOST.plist file with the original LaunchPadDBName in ~/Library/Preferences/ByHost. I took that string and edited the current com.apple.dock.plist by adding two additional rows:
ResetLaunchPad | boolean | NO
LaunchPadDBName | String | <value>
Additionally, I changed the copied .db filename to <value>.db so that the .plist key was pointing to the correct file.
I then modified the LaunchPad configuration, restarted my computer, and voila! LaunchPad configuration was preserved once more!
This fix was made on macOS 10.12. It has not been confirmed to work on any other versions.