For some weird reason, I don't think you can backup from google contact by adding the account. The best thing to do if you have a yahoo account is to sync your google contacts to you yahoo contact. Then, add your yahoo contacts to you iphone. Also, you could sync them to your windows PC and then connect to itunes and sync them over.
I had the exact same problem months ago, I installed dropbox, then transferred them there and then onto an iPhone.
If you install dropbox on Android there will be a new menu in your contacts, look for it.