Since tugh is not only an adverbial but also a time expression, I'd err on the side of caution and order this sentence tugh chaq maHegh based on the rule that time expressions come before adverbials. Since Klingon word order differs from English in both adverbials and time expressions, I wouldn't rely on English order (perhaps we will die soon) to determine the Klingon adverbial order.
A fair point. I feel as though putting the chaq before the tugh stresses the potential of immediacy, rather than the immediacy of potential, but that's not really supported by anything concrete.
Your suggestion also more closely matches the canonical yIlop! wa'leS chaq maHegh! (although there we have a noun acting as the time expression, so it's slightly different).
I'll make the change, but keep both as accepted translations.
Update: I had a look in paq'batlh, and I found that we actually have examples of chaq tugh, including one involving death:
paq'batlh, paq'raD, Canto 8, Stanza 11:
jatlh 'e' mevDI' qeylIS, lop
chaq tugh batlh Heghmo'
'ej chaq tugh charghmo'
"After Kahless's words, they celebrate,
For they may soon die with honor!
For they may soon be victorious!"
Granted, paq'batlh is worth treating with an added pinch of salt, but considering this doesn't violate any known rules and considering just how closely it matches the sentence here, I think I'll go ahead and let this one stand.