reverse polarity without relay

Yes, as Oldspark mentioned, it's really about the Hfe (or gain) of the transistor.  You need to make sure that the current in multiplied by the gain is enough current out.

47K is a lot of resistance and, at 12.6vdc (key off) would limit the current to .2 mA.  For 3A output the gain would then have to be over 11,000! 

The 470 ohm resistance would limit the current to 27mA.  Still a small amount of current, but you would only need a gain of 111 for 3A output.

The idea behind the resistor on the base is to protect the output that drives the transistor and to protect the transistor by limiting the max output (again current in to base * gain = max current out).  However, if your collector transistor is sized properly it will protect the transistor.  It's actually common when using a transistor to drive a relay to drop the collector resistor because the relay will self limit the current.  I typically add a small resistor (ie 22 ohms) just in case, but it technically would be considered overkill.

Trust me, the collector resistors were added for a reason!  :)

We had a certain product that we sold for a certain car for years with no issues at all (and not output protection).  Then, we expanded the line and picked up a new car from a new manufacturer.  All of a sudden we our warranty returns skyrocketed.  It was the exact same hardware, but now we're all of a sudden seeing high failure rates?

Well, it turned out that the car had 5 wires of the same color in the same area.  One of them was the correct wire, needing a low current ground to activate it.  Anther was a 12vdc constant wire.  It just so happened the 12vdc contant wire was easier to get to, so people were tapping it, activating the product, and letting the magic smoke out.

After that little fiasco we decided that all outputs need to be protected against shorts, regardless of their function.  For relay outputs a 22 ohm resistor is used, for other (-) outputs a 100 ohm or higher is used.  For all the 22 ohm relay outputs a diode is installed in the board to protect the transistor, elminating the need for one on the coil.  Since we made the change 3 or 4 years ago our output failure rate has been virtually zero!

That's a Darlington configuration (two transistors connected in series, total gain = gain1 * gain2) with a gain of 1000.  That'll get you 250mA of current - enough to fire a relay but most likely not an actuator.  If you are only driving the cars OEM relays then you're golden!

Did you ever have any issues running that big of a resistor?