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If the new alchemy trinket works the same as old one (buff doesn't get removed even if you unequip trinket). You can force to proc it before the pull, then swap it to rng trinket(which can proc instantly)... free third trinket proc for the start of the fight.
There is some advice and help in here to get simc improved. You should check post #37
What you also need to consider with "on use" trinkets is the combat time. Their efficiency rise and falls with the combat time.