There is no way to influence the rate other than change the difference between your TH and the TH on the mob, or by using SATA which is known to provide a significant increase for that one attack.
SE has already answered this question. Even though people have argued after just a little eyeballing that crits might provide a miniscule rate increase (Those people claiming this is true say its maybe a 1-2% increase), all the crit in the world isn't going to change how people use THF, nor would it be worth doing to somehow make THF more relevant.
The far bigger issue than all of this is the simple fact that TH simply doesn't work at all in too many fights where loot comes out of chests with fixed ratios or personal rewards where TH can not be used. Frankly, if you are looking for ways to up your THF game and become more wanted/relevant in content, it's going to have to be through improving the job's damage potential.
THere is nothing out there that contradicts what SE previously said on this issue. All we have is a few people in the community who have made a suggestion of some other modifiers, but no one has provided enough data or proof that a reasonable person could conclude that such a thing probably exists.