Hi,
Using the following method I got both Defending Champion and Returning Champion in a 5-day period.
The basic method is to camp the chest on multiple servers on an alternate account, and server hop your main when an easy chest spawns.
First, get another account. A trial account works. You should also have the ability to run two instances of WOW at the same time, one for each account.
You'll make level one toons on multiple servers on the second account. They'll be easy to run to the Darkmoon arena. Use a high level character to run them out to the Gurubashi Arena, preferably one that can res. Horde is also recommended because it's a much shorter run.
Defending Champion is more difficult to acquire. Servers from the same region are merged at the Gurubashi Arena, so you have to compete with players from other servers in your region for the chest. The key is to create toons on servers in a region that's lower population. I had the best luck with Latin America.
For Returning Champion, there's no "rule of thumb" for the best servers. I ended up getting the most chests from a low-medium population server. This is likely because the competition will gravitate towards the lowest population servers.
The 3 AM and 6 AM (PST) chest spawns are easiest to get.
Log in around 10 minutes before the chest spawns. Using the second account, log into toons one at a time until you log in and don't see anyone else camping. Invite your main and hop them over to that server. Next, log out your level 1 toon (but keep your main in the group so they stay on that server!) and continue to look for another chest that isn't being camped. You do this for two reasons: First, if competition for the chest shows up where your main is at, you can quickly switch them over. Second, if you get the first chest, you may be able to quickly swap over and get a second chest.
If competition shows up, just leave and try a different server/region, unless you want to fight. However, you'll get the trinkets much faster by avoiding fights. Even if you think you can win, you can often get two chests in one spawn if you avoid fights, something you can't do if you're involved in a battle. Also - don't stealth! Your presence will often drive others away. If you stealth, you're making it more likely that others will camp.