Moving steam games
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Solved by spenser_l,
Go to your current C:\Program Files\Steam\SteamApps\common folder, and copy all of the game folders you want to an external hard drive.
Then where ever you want to reinstall these games (I'm assuming on a new computer/fresh install), install Steam. Then copy over the game folders from your external drive to the new and empty SteamApps/common folder.
Then go into Steam, and try to install the game from your library. It will detect your local files and download anything that might be missing. From there you should be good to go.
For a more detailed explanation I'm sure there are Steam forums with users asking the same question.
EDIT: Disregard my previous steps, I misread your question. Your method should be fine:

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