A comment on my Reddit thread told me to submit this on XDA, so I will also post this here and provide support for those who know how to give me proper logs of their problems.
The official Pixel Launcher has a lot of exclusive features like the Google Now panel and G Search Pill that only work while it is running as a system app. When regular users install the APK file they get a gimped version of the app that refuses to give them these features. However, after seeing the ParanoidAndroid commits to get the Google Now panel working I realized these were not limitations of being installed as a normal app, instead Google intentionally made it work this way, most probably to keep the features exclusive to the Pixel phones as a selling point like HDR+.
So, I set out to learn about AOSP's Launcher3 and Pixel Launcher. I decompiled the Pixel Launcher's apk and spent many days glued to my screen trying to import the code into Launcher3. Along the way I found that a great developer who calls himself DeleteScape was also working on this, so I PM'ed him on Telegram and he shared some of his findings with me. I used part of his deobfuscated code and it helped immensely in doing this. Shout-out to his LawnChair, whose source is available here: https://github.com/Deletescape-Media/Lawnchair
One of the limitations so far is that the app needs to have the same package name as the Pixel Launcher or else it isn't able to use the Pixel's weather widget. This will mean the well-known launchers like Nova will most probably not use it, because that would mean they could not publish on the Play Store anymore.
The A-B tests and the microphone icon are not included, so what you see is what you get. There are no toggles for any of the features. Here is a gif of the launcher in action: https://giphy.com/gifs/3oKIPu10p9eLoRc3Kw
These are all the changes into a few simple commits for other Launcher3-based launchers to import: https://github.com/amirzaidi/Launcher3/commits/master
What is working
Google Now page
G Pill animation
Google's weather widget next to the G Pill (enable location and refresh Google Now to make it show up)
Swipe up everywhere to open the app drawer
Date widget with correct format for all Launcher3-supported languages
Pixel accent colours on any device
Update Google Calendar app icon with the date
Remove Voice Search and Wallpapers from app drawer
Use the Wallpapers app when available to select the wallpaper
The latest release can always be found here: https://github.com/amirzaidi/Launcher3/releases
Anyone who wants to is free to fork my project and release his/her own version, as long as they either keep their own git open for others to see the commit history, OR provide me credits in their closed source release logs.
Top requested features I will probably not implement: dark mode, swipe down for notifications and icon pack support. Why? They are not in Launcher3 or Pixel Launcher.
READ BEFORE POSTING ERROR LOGS
If the app does not install, ensure you have deleted the official Pixel Launcher from your device. If it crashes and you are on a Samsung device, disable Secure Folder and try again.