Before you make any decisions, you need to read the details of your current plans that you might COBRA. I know expats who use Blue Cross overseas so I assume some Blue Cross plans must have good overseas benefits.
It is a real bonus to have an insurance company that handles a lot of overseas cases. I am told that even companies that theoretically can cover you overseas often freak out when your hospital reports and prescriptions are written in a foreign language, when the drugs aren't exactly the same as a US doctor would prescribe, and when your bills are in a foreign currency. My insurance company is very comfortable with these things, but I usually end up paying my bills out of pocket and then being reimbursed by my insurance company because they aren't set up to do direct payments with doctors and hospitals around the world.
You should also look hard at where you'll be traveling and whether you will want to have medical evacuation coverage. Even if you have pretty good general insurance coverage overseas, it might not include air evacuation from remote areas or across international borders to get you to a hospital with the services you need. This might not be an issue where you plan to travel, but if you need it, there are some specialist companies that provide medevac coverage.
As an American, even if I had a travel insurance policy for my year traveling, I would be reluctant to let my US policy lapse. It would be a real nightmare to have a heart attack or cancer overseas and then have trouble getting insurance when you come home.