~ "Prevarications" is a correct word for this, but somehow it felt like too expensive of a word for the rest of the poem. It seems to me to be a five-dollar word among three-dollar words—haughty, I guess, is the word I'm looking for.

~ Immediately on the heels of the above, "genuine honesty" is repetitive. Honesty is, by definition, genuine. I rather think the modifier could be pruned without damaging the line.

"Daily Flash Fiction Challenge"  - This is good for learning how to be very succinct. You have to tell a story in 300 words or fewer.
~ "The Writer's Cramp"  - This is great for getting good at thinking fast—an entire short story in 24 hours. (This is one I'm struggling with right now...but it's fun!)
~ "I Swear I'm Cool Somewhere!"  - This is a fun forum for letting your imagination go, but capturing the good time on paper (or on the screen, as it were).
~ "The Adam West Conspiracy"  - This is a contest I host. You're welcome to take a look and see if you want to play along.
~ "The Contest Challenge"  - Last one. This is kind of a hub for several different contests.

~ I think your presentation of verse might be better achieved by using a more classic mode with line breaks offering rhymes at the ends of each line. The reader finds the rhythm and the rhyme, and has a hard time focusing on the story because he is constantly trying to catch that rhythm throughout the lines.

~ Your rhythm is irregular throughout. It holds to a loose framework, but it's like a flight of steps where some risers are less even than others: the reader trips and stumbles over some of them. Perhaps working with classic line breaks, as mentioned above, would help identify areas of opportunity to even out that flow.

~ There's some punctuation that can be tightened up. Although, at the same time, most of it is spot-on. But some of it did trip me a little, so I wanted to mention it for your own reference.

~ In your story, the innocence of Naomi is nicely contrasted against the crew's rather less-than-innocent interpretations of the scene. We find ourselves eager to eavesdrop on the officers, as well.

~ The Vulcans behaved more passively than one would expect. Their lines seemed to be inconsequential, just a way to throw some Vulcan lingo into the mix.

~ The crew outside the door was borderline insubordinate in their behavior. I know it was for effect, but accidental eavesdropping might have been a better fit a starship crew.

~ Janeway's ire was very well played. A good commander will show her emotions, but will not inflict them on others.

~ The middle part, which is certainly prose rather than poetry, is begging to be reworked to fit the rest of the poem. It's where the turn is, where the absolute most important part of the poem is (except for that wonderful third line).

~ You might also consider letting the second to last line go away. "Stupid" just doesn't fit the rest of the vocabulary in the poem. It sounds argumentative and petulant compared to the rest of the pointed, deliberate verbiage.

~ This is totally this reader's opinion, right here. Consider single-spacing some of your lines together, like stanzas. Let them capture complete thoughts—not terribly unlike that middle paragraph, only grouped as lines.