Here, I come drinking the Kool-aid again, but I must say, some of these answers miss the point. I keep hearing about rewrites and server mods, which is dancing around the point at hand.
You have a large site and you're having issues making site-wide updates.
So first, can we address what might fix THIS problem before we move on to the pros and cons of what might fix this problem?
You have two choices.
1. Go dynamic using a programming or scripting language.
2. Go dynamic using a CMS program.
A simple way to use programming would be using "includes" for a header and a footer. Your index file would look something like this
This would allow you to change the header and footer on the fly for the entire site. You can also use other includes for "snippets" of code and advanced functions. Only then could you consider the advanced server options to handle the file names. 1) 301s to change .html to .php or 2) rewrites to keep the .html with php functionality.
<?php "path to file/header.html");?>
The body of my document
<?php "path to file/footer.html");?>
Your other option is a CMS system. I don't know the constraints you refer to, but I would SERIOUSLY consider a CMS system. Something like Wordpress would allow you keep keep full control over file names, code, design, etc. The benefits that I see for you and the company are: WYSIWYG editors for you and your internal clients. The ability for users to create, modify their OWN pages. This leaves you free to pursue higher goals, removes you as a perceived friction point to employee's who wish to create and modify content. Allows for a huge amount of flexibility without a build out. Other Open Source options would be Joomla or Drupal.
If anyone has any feedback on these two methods or my logic I'd appreciate it.
FYI: I just did one of these conversions with wordpress at the beginning of April. I used 301s to forward all .asp to .php. My case was a little different because it was dynamic to dynamic. My goal was to make adding content easier though the use of a CMS. I was able to add advanced functionality, keep the SEO file names, the SE rankings and my sanity.