Moving Logic Pro To New Macbook

I recently moved Logic Pro 9 from my previous MacBook to my new one by copying over all the files from my old MacBook to my new one. However all of my Logic Pro files are now duplicated twice: once on my hard drive library and once on my user library. Although everything works, I do not like having Logic take up double the space on my computer, and it's bothersome and confusing to see 2 sets of every logic instrument in my drop-down windows.

I tried clearing everything off the hard drive, but then Logic wouldn't open. So I moved it all back to my hard drive and tried clearing it from my user library. Logic opened, but a lot of plug-ins and functionality were missing.

So I've gone back to square one: all files copied both to my hard drive library and my user library. Everything works fine, but as mentioned it is not ideal having Logic take up double the space and show all instruments twice.

Apple Support e-mail told me to try re-downloading it from my App Store purchases. I see it in there, but it just says 'open' - no option to 'download'. Perhaps this is because it recognizes it's already on my computer. Is there a way for me to completely clear it off my Macbook and start over?

Please provide any suggestions.