Thank you, SuStel, for your reply!
This is {-'e'} used for focus. Here it is with helpful punctuation:
Dung qo' lupawDI' chaH, qeylIS qorDu'Daj je ta''e' neH bop bommey. As soon as they arrive in the upper world, it is only about the deeds of Kahless and his family that songs are about.
(This is awkward grammar in English, but in Klingon it is just the addition of a syllable.)
But why *-'e'* and *neH* together? Wouldn't just *neH* translate as you propose?
This is also focus. Adding punctuation and a bit of helping brackets:
veng 'elDI' ghaH, [pawpa' ghaH'e' paw lutDaj 'e' Sov qeylIS]. As soon as he enters the city, Kahless knows that his story arrives before HE does.
The first subordinate clause is a subordinate clause to the entire line. The second subordinate clause is a subordinate clause of the first sentence of the sentence-as-object construction.
Put another way, in the sentence as object, sentence 1 is {pawpa' ghaH'e' paw lutDaj} and sentence 2 is {'e' Sov qeylIS}.
Yes, reading it so is helpful. I think I was just fixated on interpreting focus literally as "THIS and not something else", while it is more about emphasizing a noun out of whatever reason it may apply (here, e.g., because it is surprising and unexpected). A last question: I don't want to reopen a long discussion about aspect, but wouldn't it make more sense to say *pawpu' lutDaj*?