Sierra Frozen at Login Screen – Keyboard and Mouse Unresponsive

After rebooting my MBPr, it is now frozen at the login screen showing the list of users. I'm unable to move the cursor or use the keyboard. Booting in safe mode does the same thing. A few days ago, I updated Sierra to 10.12.4, so it might be related to that. Right before the problem happened, I was pruning old third-party Launch Agents and Daemons, but I did not delete any from Apple. That might be related, but I don't know for sure, since I very rarely reboot the computer.

I reset NVRAM.

I deleted /Library/Preferences/com.apple.loginwindow.plist.

I used Disk Utility in recovery mode to repair the startup disk, but no problems were found.

I looked at /var/log/system.log using Terminal in recovery mode, and I see many lines related to Installer, so is it trying to install something, or is this a normal part of recovery mode?

Small sample of the log is below, and the full log is on pastebin. Sierra's new log command doesn't work from recovery mode.

May 15 16:10:08 MacBook-Pro Installer Progress[151]: Register process 491, phaseName Install Springboard, uuid 35F782F8-715E-41FF-9AF6-DB016B483C68
May 15 16:10:08 MacBook-Pro Installer Progress[151]: Connected processes = {
        "35F782F8-715E-41FF-9AF6-DB016B483C68" =     {
            "Phase Name" = "Install Springboard";
            "Process ID" = 491;
            UUID = "35F782F8-715E-41FF-9AF6-DB016B483C68";
        };
        "A9879B21-4872-49FC-AC94-E8F7985A5F61" =     {
            CompletionHandlerKey = "<__NSMallocBlock__: 0x7fe35dcf0580>";
            "Phase Name" = "Language Chooser";
            "Process ID" = 468;
            UUID = "A9879B21-4872-49FC-AC94-E8F7985A5F61";
        };
        "D963D32E-BA49-4ADD-8359-79B93262F438" =     {
            CompletionHandlerKey = "<__NSMallocBlock__: 0x7fe35b70eb50>";
            "Phase Name" = "Launch Progress Window";
            "Process ID" = 465;
            UUID = "D963D32E-BA49-4ADD-8359-79B93262F438";
        };
    }
May 15 16:10:08 MacBook-Pro Installer Progress[151]: Saving completion handler for phase Install Springboard
May 15 16:10:08 MacBook-Pro Installer Progress[151]: The Progress UI has been hidden
May 15 16:10:08 MacBook-Pro Installer Progress[151]: Saving completion handler for phase Install Springboard
May 15 16:10:08 MacBook-Pro Installer Progress[151]: Unregister process 491, phaseName Install Springboard, uuid 35F782F8-715E-41FF-9AF6-DB016B483C68

I appreciate any advice, but if you simply tell me to reinstall MacOS, I will downvote the answer, because I want to actually find the problem.