Excellent choice!
That's the way to do it! No lossy transformers, bridge rectifiers, etc, just straight off 12V. I have seen these things before. They have an instant, full brightness start-up with no flicker. I would get mine from Rockby (factory surplus) Electronics in Victoria (very cheap new parts, wide variety and usually on special too).
http://www.rockby.co...chkey=led strip
Do they get warm after they have been running for a while? If so, they might need to be Liquid Nails'd to a length of aluminium and then onto the timber.
Are yours the "plug and play" type? How many can you run on your current system? There are much brighter and more efficient LEDs available, but for the money, what you have is certainly a step in the right direction.
When in college, we found that LEDs are much brighter when pulsed and take a lot longer to drain the batteries. The good thing about that, is that if you pulse them faster than 90Hz, the LEDs appear to be permanently "on" without any flicker due to our persistence of vision.