The discussion in viewtopic.php?f=2&t=25807 made me pretty confident that TH is a debuff, that the party the THF is in doesn't matter. But in an Arrapago run the other day, I noticed the following:
TH3 in other party: 3 cells from 5 lamiae
TH3 in killing party: 10 cells from 6 lamiae
We moved the THF into tank party part way through 1st floor not for TH, but so they'd get songs instead of the (so far) weaponless SAM. But the difference in drop rate was quite dramatic and immediate...