What would be the best way of reporting the sale of ESP shares acquired 10+ years ago when I don't have the specifics that would normally be detailed on Form 3922?

If you know when you acquired them you should be able to put together a really good approximation of the 3922 from the time you acquired the shares.  The value of the shares and the historical information regarding them is public information.  

You should also be able to contact your company for ESP information - they should be preserving that.

@dpitera36