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

I have a lot of online accounts, web services, and so on -- personal as well as business -- so obviously(?) I use a password manager to handle them all. Specifically I use Lastpass but my question applies to any and all:

Given the Heartbleed problem and related questions, even if I wanted to change all my passwords (and shouldn't we all be doing that at regular intervals??), how in the world can I change so many passwords in an efficient manner?

If I have to visit each service and site individually and change the PW manually, it's clear that it will take a weekend of dedicated work ... password security is good and all but that's just not practical.

_{Update: I just used Lastpass's "security challenge" which reports that I have 274 sites and a security score over 83%. Several intranet sites at work reuse the same pw which significantly lowers my score. All my Internet accounts score above 92%.}

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.