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 in Japanese. In creative writings, you may say
I dirtied the words.
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:
.... the words which I dirtied (a noun phrase with an object marker, without a verb)
... the words that have dirtied (i.e., dirty words)
... 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?). 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:
Gimme money! / I need money!
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:
(lit. "You who is gazing me and smiling at me")
You are merely gazing me and smiling at me.
We are maidens with our hearts armed with steel.
Keep in mind that these are merely noun phrases without corresponding verbs, grammatically.