Intel HD graphics driver ver 8.15.10.2900 on my HP pavilion DM4 which has been upgraded; win 7 -> win 8 => win 8.1 with only minor glitches (finger printer reader took some hands on to get It to work under 8.1)
My previous issues this thread, was an HP envy 23 all in one touch screen which also contains an Intel HD graphics driver and a simple win update to the latest Intel HD graphics driver version solved my 8.1 install issue, as documented this thread, witht he envy 23.
Give that I have different hardware all around, my advice is of little help to your situation.
Depending upon how persistent you choose to be, given that you have correctly narrowed the issue to an intel driver and you have correctly identified that SOME existing intel driver will work on 8.1 with your hardware platform, the 8.1 goal is obtainable, but I can't provide you a path to the goal.
David