How to create an email with embedded images that is compatible with the most mail clients

Question

I’ve had success with exactly the same headers as you’re using, with the following differences:

Embedded is not a valid value for the Content-Disposition header. attachment should be fine. inline should also be fine, though I’ve usually seen attachment for multipart/related embedded images.
The value of the Content-ID header is supposed to be in the same format as a message-id, which in turn looks very much like an email address. <083.gif@yourmailer> has a better chance of working with most mailers.