Update: The par score for The Great Journey is now a measly 8,000 points. So play on Normal with a handful of skulls or Heroic with a couple skulls and you shouldn't have much of an issue.
I did this on Heroic
with 7 active scoring skulls: Anger
, That's Just... Wrong
, and Thunderstorm
. I completed it in 15:55
, which is 55 seconds over par time and I finished with a score of 45,355
. The run before this I did not have the thunderstorm skull on and finished the level with 24,168 points :( You can probably do this with one less skull, but it would have to be a near flawless run.
I uploaded my Twitch broadcast to YouTube here. Apologies for overlaying my face on the scoring UI... You can skip to 20:01 to see my final score.
From the start, you'll need to hijack a ghost because the jacked skull is active. This can be a real pain. Try to use your camo to get close to the brutes in the ghost, but since the That's Just... Wrong skull is active, they will know you're there anyways. In my video, I cut out about 6 minutes of me failing to hijack a ghost.
Near the beginning of the level, you can de-spawn the two wraiths guarding the doorway by backtracking far enough.
After you meet Johnson in the scarab, you can de-spawn the three wraiths you would have to kill by going back into the room you came from and hitting a loading zone.
At the end, I shot the wings off my banshee so that I could fly it inside the room. You'll need to exit the banshee in order for the door to open, but then you hop right back in.
You can find commentary and more explanations of these tricks in Naked Eli's speed run.