Damn, I should have tried that. It's how strafing works in my game too.
Anyways, here's the playthrough: Haunted and Hallowed Pt1 by MScull
I had quite a lot of footage, so the first part is my initial playthrough, and the third is my final.
The middle one is all the other attempts sped up with some music. I didn't wanna upload it all in full, but I thought you might wanna see the evolution of all the routes I took. Maybe too fast, but it should be readable at half speed.