The rule hasn't been spelled out in canon, but based on the examples we do have, it depends on if you're using HochHom to mean "most (of the people/things)" or "the greater part (of something/somebody)".
qIj Duj HochHom. = "Most of the ship is black."
You might say this of a ship that is 80% black.
qIj HochHom Dujmey.= "Most of the ships are black."
You might say this of a fleet of ships, 80% of which are black.
HochHom consists of the word Hoch ("all, everyone, everything"). Its use for counting things is explained in some detail here: http://klingonska.org/canon/1996-06-holqed-05-2-a.txt
We have plenty of examples of it being used in this way, for example:
DujDaj HubtaHvIS Hegh 'e' tul Hoch tlhIngan. = "To die in the defense of his/her ship is the hope of every Klingon."
Hoch 'ebmey tIjon! = "Seize all opportunities!"
There is also at least one example of it being placed after a noun to suggest the entirety of that thing:
muptaHvIS tay''eghmoH QeHDaj Hoch ~ "all his rage focused into one blow" (or, more literally: "While he struck, his anger's entirety united itself.")
With HochHom, we don't actually have any examples (that I know of) of it being used to count things (i.e. HochHom Dujmey). In fact, we only have one canonical sentence using HochHom:
tera' vatlh DIS poH cha'maH wej HochHom lo'lu'taH. ~ "It [the k't'inga battlecruiser class] remained in use for most of the 23rd century."
It's not much to go by, but it makes logical sense that HochHom would follow the same pattern as Hoch, and what little info we do have on it seems consistent with that, so that is how it has been used in the course.
Thanks for the detailed explanation! Even though that's a lot, I think I can condense it to something portable enough:
Hoch before the noun every/all x (sing./pl.); after the noun the whole x
HochHom before the noun almost every/all x (sing./pl.); after the noun almost the whole x
It's a little sloppy, but I think it'll get me through the workday.