In which "Extensions folder" are you looking?
If the the iGPU-NVRAM variable is set to correct values and AMDRadeonX3000.kext is not in /System/Library/Extensions then you should be able to boot into the full OS.
Please re-check in your safe-boot Terminal.
Type:
$ sudo nvram boot-args="-v"
# to enable verbose boot
$ /usr/bin/find /System/Library/Ext* -iname AMDRadeonX3*
# to find the troublemake kext
If that doesn't turn up anything, take a bit of time and wait for the following command to finish:
$ /usr/bin/find / -iname AMDRadeonX3000.kext
Memorize the output of the above command for the location as /path/to/your/kext.
The hang on boot is likely because the X3000 kext is present in a folder where it is auto-loaded at boot.
--> If SIP is currently enabled, and let's just assume it is:
Boot into SingleUserRecovery: holding <Cmd>+<r>+<s> on system start.
Type:
$ csrutil disable
$ reboot
Boot into SingleUser: <Cmd>+<s> on system start.
$ mount -uw /
$ mv /path/to/your/kext/AMDRadeonX3000.kext /AMD_KEXTS/
#### adjust the paths to what you found above and to what you did 2 months ago; after 10.12.6 update the /path/to/your/kext/AMDRadeonX3000.kext will very likely be: /System/Library/Extensions/AMDRadeonX3000.kext
$ sync
$ reboot
You should now boot verbose mode into an iGPU accelerated Sierra normal full boot.
Thank you! I figured out the issue. Your post gave me the idea. I did find the x3000 in extensions, but could only see it with the find command for whatever reason.
So now I knew my problem. Despite what I was typing, it was not moving. I was trying to move it to the directory I created two months ago. I thought maybe it is refusing to overwrite and not moving. I created a new directory. I moved the file there. I confirmed it moved with a find command.
I restarted once (in verbose), made it past the lock screen freeze, but then it rebooted. On the next go I got into OS X without safe mode!
Thank you to everyone that helped. I've also learned a ton about unix commands from you all.
I reactivated SIP and restarted and it works again.
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