Can you unstick a stuck tire cap for less than 71 bucks?

Dear Tom and Ray:

I took my 2008 Audi A4 for routine maintenance. The dealership informed me that they could not check my tire pressure, because I had "aftermarket valve-stem covers." I was confident that I didn't, since I'm a "Suzy Homemaker" type and never added anything fancy to the car. But then my husband strolled in and admitted he had bought some blingy silver-bolt decorative valve-stem covers at the local big-box store without telling me. I'd never noticed. Anyway, the dealership said these caps are now rusted on, and there is NO WAY to remove them. They say they can saw off the stems and replace them for $71 per tire. Can this be true? Seems like an expensive mistake. Should I try pouring Coke on them (like we used to do with batteries)? Someone said to apply heat. What do you think? Thank you for any ideas.
-- Jane

Tom: Those valve-stem caps your husband bought -- with the pictures of Pippa Middleton on them -- were made of some really cheap metal. And they've now rusted to the threads on your valve stems.

Ray: The reason they cost $71 apiece to replace is that there are tire-pressure monitoring sensors in them. If the sensor in the valve stem detects low tire pressure, it sends a wireless signal to the computer, which activates a warning light on your dashboard. And now the shop has to remove those sensors and put them in the new valves, which is why they can't just throw a set of $5 stems in there and call it a day.

Tom: But I wouldn't cut 'em off just yet (and, just to be clear, I'm referring to the valve stems, not your husband!). I'd try a penetrating oil, like Liquid Wrench, or some other product that's supposed to break down the rust bonds.

Ray: Try one wheel at a time. Get the wheel lined up so that the valve stem is pointing down. Then drip or spray the penetrating oil onto the valve stem, and let it run down under the cap. Be careful not to spray the oil all over your brake rotors, because that makes the car very hard to stop.

Tom: You can apply the penetrating oil several times during a 24-hour period. The longer it has to work its way in there, the better its chances.

Ray: Then take two pairs of vice grips. Hold the stem with one pair so the rubber part of the stem doesn't twist, and grab the rusted-on cap with the other pair and turn it.

Tom: I think it may work. Your dealer doesn't want to take the time to do this, but you might as well give it a try.

Ray: Right. If it doesn't work, you're no worse off than you are now. And -- needless to say -- if you do get 'em off, throw them into the garbage immediately. Good luck, Jane.

(Car Talk is a nationally syndicated column by automotive experts (and brothers) Tom and Ray Magliozzi. Write to them at the Car Talk website.)