What, were “The Prostitute Doctor” and “The Princess Plumber” already taken? Too soon for “The Cowboy Interior-Decorator” or “The Oscar-winning Idol-loser”? Any of these titles would have worked. As “The Astronaut Farmer” progresses through its veiled and interesting plot of self-actualization, an initially puzzled viewer learns that it’s not just about a NASA-trained plowman. It’s more bizarre, more powerful, more symbolic than the kind of simplistic tear-jerker its misleading trailer would have audiences believe.

If the film is meant to fit easily into one genre, then it most certainly fails. For a comedy, it’s not funny enough. For a drama, it relies too heavily on hyperbole and suspension of disbelief. And if “Astronaut” is intended for children, then the absence of both animation and talking animals is a hurdle it cannot even hope to clear. But if the strange, ambitious choice to set beautiful scenes against a plain backdrop “somewhere in Texas” is permissible in a film starring Billy Bob Thornton, then “The Astronaut Farmer” might just be worth watching, or even re-watching.

Thornton plays a farmer named Farmer — the first hint that some bigger, less-attainable meaning lurks behind the seeming simplicity of the narrative. A former astro-cadet who left training to cope with his father’s suicide, Farmer literally aims high when he decides to build a rocket — “bolt by bolt” and with the help of what Bruce Willis’ cameo calls “some serious engineering” — in the low-tech facilities of his barn. Farmer’s not just going for a rickety Lego-model, but one that is fully launchable and navigable through space. He enlists his entire family — including two young girls, a teenage son and a wife (the ever-so-wonderful Virginia Madsen) — to assist him with the project. It is, of course, against federal regulations to launch an Apollo mission from private property, so Farmer runs into trouble with the FBI, adding to the obstacles that stand between him and his dream.

For one, Farmer ain’t got no money. His loving, dedicated wife waits tables at the local “Calf-A,” dishing out breakfast specials that cost $2.99, while he tills the land in a space suit. When the local bank threatens to foreclose on his mortgage, Farmer throws a brick through the building’s window, thereby involving the entire town in a debate over whether a man who dares to defy impossible odds ought to be celebrated or certified insane.

Madsen is perfect for the role of Farmer’s wife because she has a strong sex appeal — emanating partly from her maturely feminine voice and partly from her large breasts — that adds to a thoroughly sympathetic and yet hard-to-understand character. The scene in which Mrs. Farmer learns of her family’s bankruptcy while standing in line at the grocery store shows her wearing a heartbreaking look of concealed shame that produces enough raw emotion to sustain an entire episode of “Grey’s Anatomy.” And things only get better, as Madsen’s character tears herself apart in scenes of gut-wrenching tension, only to wake up the next morning having internalized all of it.

Admittedly, the film’s script — about chasing dreams and defying expectations — can be as cheesy as a hunk of moon rock, but it thankfully carries little enough gravity to drag the entire film down with it. This is in part due to Polish’s choice to let the camera do the talking, like in the final, stunning scenes of Farmer’s triumph.

But let’s face facts: “The Astronaut Farmer” has nothing going for it in the realm of marketability. The title itself causes eyes to roll among thicket-dwellers and Ivy-League-educated engineers alike. When a film seeks, like this one does, to defy genre — or the set of expectations an audience has based on buzz and other marketing tools — it risks alienating everyone. Call it crazy or call it genius, “The Astronaut Farmer” at least deserves props for taking one giant leap in the direction of originality.