How to express this idea?

[Zvarri]

"sharpen the saw" -- to hone your talents to perfection, add the finishing touches, polish your skills

I feel like the three examples lack the simplicity that the image of "sharpening" the saw gives.

Are there any other similar images like sharpening the blade, etc that you could come up with?

[phantomkitsune]

Context would be useful here, but honing refers to giving something an edge in metalworking, so I think it best encapsulates what you're trying to communicate.

Whet might also work - to whet one's wit is something I've heard a few times, but in company that is entirely too fond of homophones.

[Pseudo-Onkelos]

This has more to do with character, but there is the Hebrew proverb, "As iron sharpens iron, so one man sharpens another."

[twinks and bears]

You generally hone, polish, or add finishing touches to something to make it look better or be of better quality. You sharpen a saw to make it safer and easier to use.