ADRStudio -- You're a godsend!!
After reading your post and muddling about with my PC a bit, I finally managed to make it to 8.1 myself (after a week of failed attempts) ... THANK YOU :)
I have an HP Envy M6-K025DX, and like you said, the HP Drivers seemed to have been the problem with me as well. I followed your instructions, but there is one difference -- Unlike in your case, try as I may, the Intel HD graphics driver kept getting auto-installed after I removed/restarted on Windows 8. To work around this, I tried changing the device installation settings as well, but nothing helped.
Finally, what I did was first uninstall the Intel HD drivers, and then INSTEAD OF RESTARTING, I went ahead directly with the Win 8.1 store update (like you said, it had already been downloaded for me earlier so I did not have to go through the pain of re-downloading). Lo and behold, the upgrade to Win 8.1 happened without a hitch.
After upgrading to 8.1, I checked my graphics driver, and this showed the default MS Graphic Driver. As suggested by you, I had already downloaded the 8.1 Intel HD driver from the manufacturer (HP) site, and went ahead with the driver install ... Again, worked like a charm, and I am successfully on 8.1 as of now with no issues seen for the moment!
Thanks again, and hope other folks have luck with this **painful** upgrade!