Don't tell other posters what to do. If you have a problem with a post, report it. Also, I'd be careful about pointing out other people's flaws when your post isn't quite perfect either.
I don't think I have ever seen any information about whether putting a trinket into a slot resets it's INTERNAL cooldown. (It certainly works for on-activation cooldowns.)
Test it for yourself. You probably don't need to go so far as to exchange your trinket, you can just pop it out & then in again, start your meter, and beat on a dummy for a while. I'd be curious about the effect as well.