Genie said (s)he doesn't mind near rhymes and I agree. Some times bad rhymes make a good song work. Fred Eaglesmith is one songwriter who puts the story ahead of the rhyme and it works (for me). The song HAROLD WILSON comes to mind.

I had me a place on Thunder Ridge in a doomsday shack
My wife she left and took the kids a couple of years back
And I spent most of my mornings just thinking about that
And my afternoons tryin' to figure out what to plant.

While "shack" and "back" are rhymes, "that" also seems to work fine.

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They sold that farm to some fool for six cents on the dollar.
I saw him out ther last week; I's on the way to visit my daughter.

Works for me.
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The government cheques come down the pike as regular as rain.
I sit out here most every night 'cept when the June bugs drive me in.

Also works for me.