I agree with Crowhugger and Mike, Old Dude, that your phrasing works fine with that song.
It is very regular and predictable from verse to verse and verse to chorus, but that's not unusual for that kind of music.
If you want to sing the story more 'lyrically" (I think that's the word), you could try modulating the rhythm a little in places. E.g., on the chorus, instead of starting with "[Rest] you can SAY," you could omit the rest and make "You" a quarter note. There are a few other places where a line or phrase might be emphasized by breaking away from the usual rhythm.   Sometimes this draws attention to the lyrics/story and away from the melody as repeated pattern.   I'd just say toy around with it -- maybe without the instrumental backup -- till you find the phrasing that seems right to you.