So actually rather often in Japanese music, I see phrases like this:

汚れきった言葉を

with some sort of verb modifying the noun, and with the noun having the direct
object particle, but no verb. I always assumed this was more of a sentence out
of order than a noun with an attributive phrase, as in "The words were
dirtied." But is it more of a noun with an attributive phrase, as in, "The
dirty word?" Is it a sentence out of order, or simply a noun with a modifier
and perhaps and inferred word?

Thank you for your help!
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syntax particle-を sentence
Strangely-Ordered Sentences vs. Attributive Phrases
I would say that this is a phrase where the final verb is omitted. We could
expect the complete phrase to be something like 汚れきった言葉を言う. But here, the
final verb is omitted, because the context of the previous sentences is clear
enough, I guess.
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First, 汚れきる is an intransitive verb, and thus 言葉を汚れきる is ungrammatical and
doesn't make sense in the first place. 言葉を汚しきる would make sense.

There is also [hyperbaton](https://en.wikipedia.org/wiki/Hyperbaton) in
Japanese. In creative writings, you may say

> 汚しきった 言葉を  
>  _I dirtied the words._
>
> ずっと見ている 私を  
>  _You keep an eye on me._

But note that there is a space (or a comma, a period, a sentence-end particle,
or whatever) separating the two phrases. If it were not for such a separator,
the phrase would be interpreted as a simple relative clause modifying the
following noun. And it's also very common to make a final predicate left
unsaid in Japanese. So:

> 汚しきった言葉を  
>  _.... the words which I dirtied_ (a noun phrase with an object marker,
> without a verb)
>
> 汚れきった言葉を  
>  _... the words that have dirtied_ (i.e., _dirty words_ )
>
> ずっと見ている私を  
>  _... I, the person who keeps watching [you]_

Many sentence that ends with を has an omitted verb related to desire/wanting
(see: [Does the particle "を" (wo) have a special use when at the end of a
sentence?](https://japanese.stackexchange.com/q/1209/5010)). Apparently this
is not the case in your example.

* * *

To translate such a sentences in lyrics, you have some options. If the omitted
verb is clear from the context, go ahead and use it:

> お金を!  
>  _Gimme money! / I need money!_
>
> いつまでも君を  
>  _I love you forever_

Another option is to forget the verb and translate it as a noun phrase without
a corresponding verb (like "Twinkle twinkle little star.") Yet another option
is to rephrase it as a "normal" sentence, just as you have done so far:

> 私だけをただ見つめて微笑んでるあなた  
>  (lit. "You who is gazing me and smiling at me")  
>  _You are merely gazing me and smiling at me._
>
> 心まで鋼鉄に武装する乙女  
>  _We are maidens with our hearts armed with steel._

Keep in mind that these are merely noun phrases without corresponding verbs,
grammatically.
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