My system is simple enough that I actually use it. Every morning I look at everything on my plate and ask two questions: what happens if this ships late, and who's waiting on it. Anything that blocks another person jumps the queue, because my delay multiplies through them — I learned that in my internship when I sat on a data pull for two days without realizing three people were stalled behind it.
When genuinely everything seems urgent, I don't privately guess — I go to my manager with a proposed order, not a complaint: “Here's the sequence I'd run these in and why. Does that match your view?” It takes two minutes and it's saved me from optimizing the wrong thing more than once.
The week that tested it was my internship's end-of-quarter crunch: three deliverables, two owners, one of me. I proposed a sequence, flagged that the third item would land a day late unless something moved, and one owner immediately said hers could wait a week. The panic was optional; the conversation wasn't.