Adding onto the previous comment, I will say that if going from a 96% to a 98% is going to take up a significant amount of time that you believe you could've spent writing a research paper then just do the research paper.
However, if you're debating between working hard to go from an 85% to a 95% or working on a research paper then try to get to 95% because colleges want to make sure that first and foremost you are able to excel in academics and that you are then also able to do other stuff outside class, but academics comes first because they want to make sure you will do well in college classes.
Olympiads are always great because they show AOs that you are taking that extra step and that you are indeed more academically accomplished than someone who just focuses on school work but again, olympiads should only be in addition to great school work and not at the cost of it.
Getting independent research published is an extremely impressive accomplishment especially if it is linked to (or is itself) even remotely groundbreaking - this is often impossible to achieve but nonetheless independent published research is a seriously impressive accomplishment - even co-authoring papers is a significant accomplishment so if possible it is something you should certainly try to do as it is a significant indicator of intellectual vitality and true passion for a subject.