"Now we fight; perhaps we will die soon."
Translation:DaH maSuv, chaq tugh maHegh.
The Klingon Dictionary describes it thus:
the adverbial precedes the object-verb-noun construction. It is possible for an element of another type to precede the adverb. Most commonly, this is a time element (a noun or phrase meaning today, at six o’clock, etc.).
When the book describes a "time element" as a noun or phrase, it doesn't rule out the possibility of a time element including a time-describing adverbial, but it doesn't sound like it's saying that. It sounds like it's saying that a time element is a noun or noun phrase. That would mean that an adverbial like tugh isn't included in the rule.
So according to all the explicit rules we know, there's nothing wrong with this sentence. However, to be safe I would do it the way you suggest: tugh chaq maHegh. That way, whether time-based adverbials count as time elements or not, it works.