import gmail to outlook.com

I decided to switch to outlook.com from Gmail because I use outlook 2013 and the exchange connection is far superior to IMAP.  Exchange also supports syncing of tasks, calendar, and just works better.  The problem is I have many saved emails in folders in Gmail and it appears the only way to import them is all together in one large mass, no folders, no saving to those folders, just over 5,000 emails in one folder.  I thought I could just copy messages from the IMAP folders to the exchange folders in outlook 2013, which would then sync with the outlook.com server.  I keep getting an error message saying "Exchange ActiveSync doesn't support what you're trying to do"  If I cannot get my mail in the existing folders in outlook.com then it's pointless to make the switch.  I don't have the time to go through 5,000+ messages to sort them.  Any suggestions?