How to convert a 1.4 minecraft world to 1.7?

I finally found an old save file I thought I lost when I had to reformat my computer. My wife and daughter are getting into Minecraft now and wanted to show them the world I had spent so much effort making.

I think its from the 1.4 era (wolves had just been new). I drop it into my.minecraft/saves folder with the other worlds, and can see it. It says last played 3.31.11 and Must be converted!

However, when I select Play the game crashes out and when I select Re-Create the game crashes out.

I noticed that the folder with my world has slightly different files than the worlds I created via 1.7, but adding copies of those files to my old world's folder does not make it playable.

Maybe, using the launcher, you can run previous versions of Minecraft, starting with 1.4 & moving forward, each time loading your game world, so to gradually convert it forward?
I don't know if it will work, but it's worth a try.