MovieTexture cutscene - performance issues (stuttering) in Unity5

I'm using uGUI Raw Image component to play 720p .ogv (Theora) video, 31 seconds long, 45MB of size, using Unity 5.1.3. My setup is like this:

The CutscenePlayer assigns the MovieTexture demo_intro_cutscene_720p to RawImage.texture and calls Play().

This indeed works, but I experience very noticeable stutter of the cutscene - in the Editor and in the build too - and I can't seem to find any way to mitigate this. I've tried setting the Quality of the video (in the import settings of the video asset) to 0, but it doesn't help with the stutter at all and honestly, I can't even see any quality difference on this setting.

Is there anything I can do to increase the performance? My computer runs other 720p videos with no problems.

Things I've tried so far (to no avail):

• lowering the Quality of the video in import settings of the video asset

• using Plane object to play the video on, instead of uGUI's RawImage

• just calling Play() on MovieTexture and rendering it via GUI.DrawTexture() called in OnGUI() method

• creating a clean scene containing nothing but the cutscene player to see if other objects/scripts don't cause this performance loss

• turning the VSync off - not sure if this is even supposed to change anything about the cutscene performance

Many thanks!

Edit 1:

Here's the CutscenePlayer script:

 using UnityEngine;
 using UnityEngine.UI;
 
 public class CutscenePlayer : MonoBehaviour
 {
     public bool EnableLogging = true;
     public MovieTexture Cutscene;
     private RawImage ThisRawImage;
 
     void Start()
     {
         ThisRawImage = GetComponent<RawImage>();
         ThisRawImage.enabled = true;
         ThisRawImage.texture = Cutscene;
         Cutscene.Play();
     }
 }

Also, while checking FPS with this script I've noticed the FPS is around 30-60, 30 in the time positions where it stutters most.