Pattern Search and Replace

My site is using WordPress as a backbone for our static content. All of our articles and static pages retrieve their content from our WordPress installation. We have a problem running rampant through our content. A huge amount of pages have issues with <strong> tags appearing with in <h2>,<h3>, and <h4> tags. I need to remove these strong tags, and I am looking for a way to do this effectively. Here’s a breakdown of what I want to do:

Find html formatted like <h2><strong>...</strong></h2>
Replace with <h2>...</h2>

I can’t do this with a simple search and replace because there may be situations that would cause issues. Some examples below:

<h2><strong>...</strong>...</h2>
<h2><strong>...</strong><strong>...</strong></h2>

An ideal way to go about doing this would be to have a plugin that will search for html patterns. An alternative way of doing this could be to use a standard search and replace that allows me to manually review and replace each search result.

Any suggestions?