Convert Youtube iframe to embed link

I’m working on a site that has a few thousand YouTube videos in their older posts that are inserted using the iframe. Each iframe specified the width/height, and when the site was switched to a responsive layout the videos got extended off the screen when the posts were viewed on a mobile browser.
I’m using the Responsive Video Embeds plugin now, which works fine for the videos that are inserted using the WordPress Embeds method.
So, I’m wondering if there’s an easy way to replace the old iframes with an embedded URL?
From what I have been able to find it doesn’t look like there is an easy way other than editing each post, but like I said there are thousands of videos and that will take forever.
Any help would be appreciated.