I wouldn’t get all caught up in trying to figure out “exactly” what strumming pattern Jake is using. The reasons are many. 1) Since the pattern is not really repeated the same way more than maybe twice you would basically be trying to learn this one really long strumming arrangement. 2) Jake himself never plays it the same way twice. He plays some parts of that section the same but as a whole it’s different based on the way he is feeling musically at the time. One fretting hand example is the pulling off to the open strings that happens at 3:03 and 3:07 rarely occurs in his other versions/videos. 3) I’m just not sure anyone is really capable of figuring out and notating or explaining every strum, triplet, percussive chunk as it is played in this video (even if you slow it down). I doubt our beloved Aldrine could even do this (mainly because he doesn’t have the patience to do such a thing, nor does he need to). I did the best I could when I transcribed that video version but it, without question, is not a dead on reproduction of the song because there simply is no such thing.
With all that being said, I tried your version of du ddu uu d and it works fine. I know I play it different all the time and tried to examine what I do and I seem to start it with d ddu u ud a couple of times and then just change it up from there. A mixture of these two also works great. The more important thing is to make sure you are changing the chords and working through the progression with the right timing. If you do this it really won’t necessarily matter how you strum it.
The only part of the section you are referring to that I think he uses only the index finger for is the climax at 3:29 and it’s possible he is using the index and middle together for more power. Because the part right before that where his hand sort of looks like it is going in a circular (more of an oval) motion he is using the thumb and index and middle fingers on the up and down strokes.
The suggestion of slowing the video and/or audio down is a good one and may help you get a couple of the different strums sorted out but my whole point is to advise you not to get caught up in that to the point it hinders you from putting your own feeling and mojo into the performance.
Good luck and sorry for the long winded response.