Do you still have the drivers for the iGPU installed? Can you try the following:
Install LAVFilters, open LAV Video Configuration, choose Intel QuickSync with all the tickable boxes ticked, and tick...

You mentioned adding a new graphics card. What is it? Also, which port are you hooking your monitor up to, the motherboard's port or the graphics card port?

Can you check out this video? https://www.youtube.com/watch?v=ifjbDOITozE Does it stutter for you?

And it still feels stuttery?

Alright. When you right click and choose Stats for nerds, what fraction do you see for dropped frames?

Anything from YouTube that stutters for you?

Have you tried disabling Flash's Hardware Acceleration as per http://www.hulu.com/help/articles/166587?

Can you post the URL of some of the stuttering streams?

Thanks. Using DriveLetterView to remove the drive letters seem to have made the changes stick over reboots, unlike with Diskpart.

Upload the file to a cloud storage site like OneDrive and PM me the link.

Sorry, by remove I meant remove drive letter assignment. I've checked and there are no extraneous recovery/EFI partitions.

It sounds like a codec issue. Can you upload 1 of the problematic files somewhere for us to test?

Problem is, as you can see in the pic I provided, Disk Management doesn't show those partitions as having letters assigned to them, and when I remove letters via diskpart, it doesn't stick over...

Please download MPC-HC and try to play the problematic videos with that. Does it stutter then?

Sorry, I should've said partitions, not drives.

Partitions like the recovery ones or the EFI ones are getting automounted for no apparent reason.

64669

You can see from the image above that random drives get drive letters assigned to them for no reason. In addition to that, I can't even remove the drive letters, unless I use diskpart, but...

Does YouTube stutter at all for you?

Also, which codec bundle did you install?