I would tend to read it as “Leader, and Chancellor of the Klingon empire,”
That's not a possible reading of {tlhIngan wo' Qang DevwI' je}. Did you mean it the other way around, i.e., "Chancellor of the Klingon Empire, and Leader"?
but reading your English translation, my natural inclination is to think “Chancellor … and Leader-of-the-Klingon-Empire.”
That's definitely impossible. The {DevwI'} is separated from {tlhIngan wo'} by {Qang}.
I have to think it through to come up with “Leader-and-Chancellor of the Klingon Empire.” That interpretation comes later.
If I described Gowron as {tlhIngan wo' Qang DevwI' je}, does it actually matter whether it means "Chancellor-of-the-Klingon-Empire and Leader" or "Chancellor-and-Leader of the Klingon Empire"? The only difference is whether his leadership of the Klingon Empire is implicit or explicit, but the resulting meaning is still the same. The reader or listener is presumed to know that the Chancellor is the Leader of the Klingon Empire.
In the interest of clarity, I modestly suggest that one might seek to consider alternative constructions when the whim strikes to pile more than two nouns next to each other. It’s not banned. There are no rules against it. It’s just that the grammar doesn’t offer much in the way of clarity to support a string of nouns that may be linked by conjunction and/or genitive/possessive relationships.
But if you cherish ambiguity, go for it with gusto. Amuse yourself and others as you see fit. It is completely within your rights to do so.
I don't cherish ambiguity, I just don't think there is any in the given phrase. I think one would have to go out of their way to be looking for ambiguity to find it there.
In contrast, Lieven's example of {vav jup SoS HoD je} is unambiguously ambiguous.
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De'vID