What's an efficient way to change my 200+ account passwords?

Honestly, there is none. Not unless they offer an API where you can do remote management on your accounts. Pick and choose. Which ones are the highest priority. Bank for example you should change. Forums and other media sites could be ranked lower and changed on a need basis.

PS: I also think people are blowing this heartbleed way out of proportion.

I'm curious what kind of answer you expect to get... A piece of software that cascades password changes over various protocols, sites, procedures, etc.? I'll bite my tongue on my opinion of the cost/benefit of actually changing all those passwords, considering any one of them could be cracked in a reasonable time frame, regardless if they are compromised. Instead, I'll recommend you gather contact information for each of these sites and services. Then send an e-mail to all of them requesting your password reset or to re-establish a new password on next login. I don't see any other shortcuts here.

Since your question probably doesn't lend itself to an easy answer, I would propose that you change the passwords of websites based on how vulnerable they make you (loss of money, loss of privacy, loss of reputation, etc.)