This is by far the fastest method I found, but this does require additional hardware not everyone may have access to. This solution requires a Windows 8 machine along with a Windows Phone.Doing this from a skill level already around 1300 I went to 1500 in less than 15 minutes!
I actually timed this with my stopwatch app on a separate phone.
That included set up time of my Windows 8 secondary accounts and some testing. You don't even have to touch your Windows Phone until the very end, everything else can be done on the Windows 8 machine. With this method you don't need to even load the games that are sent to your primary account because the stats are updated on the server. You can check the stats on your phone periodically just to make sure you're gaining skill, but other than that it's not even necessary to have the phone on.
Your primary account should be the one using the Windows Phone.
Your secondary accounts are logged in to the Windows 8 machine, they should be friends with your primary account.
1. Log in to the Windows 8 machine with your secondary account
2. Invite your primary account to a game.
3. Resign immediately.
4. Without leaving this screen, select Rematch. It's in the same location as Resign, so this goes very fast. Just click or touch the button, then hit Enter to approve the Rematch/Resignation or select it (if using touch on Windows 8) Be careful not to go too fast, I ended up accidentally blocking my primary account a few times because I hit the Block button instead of the Rematch/Resign button.
5. Repeat steps 3 and 4 until the secondary account's skill rating drops to 800.
Once the skill rating drops to 800 you'll no longer be helping your primary account by resigning as you can't go any lower and the primary account won't gain any additional skill. Repeat the above steps with additional secondary accounts as necessary. Starting from 1000 you should only need 3 accounts total. If you start higher you may only need 2.
Once you've reached about 1530-1550 on your primary account go in to a Skill Match and resign. You'll lose a bit of skill to the resignation but should still end above 1500 and this should pop right away.