Interesting stuff. I downloaded the two .eml files.
Both display fine for me in both OE6 and TBird 24.
(In both cases I had to change settings because
I normally set the default display to text only for
security reasons, which causes the images to show
up as attachments.) Both have embedded images,
so it's not an issue with remote images settings.

I haven't studied them line by line. The newer version
seems to be more complex, with more CSS. (Browsers
will generally ignore any CSS if they come across an
error, so that's a possible issue -- but a long shot.)

One difference I noticed:
The one that works is using a doctype that will display
in IE in quirks mode. HTML 4.0 Transitional. It should look
the same in all IE browsers. The one that doesn't work
has doctype XHTML 1.0 Transitional. That should display
in "almost standards" mode, which means it will vary
depending on the IE version. See he

https://hsivonen.fi/doctype/

I don't have reason to think that's the problem, but it's
easy enough to test: Edit the .eml file that doesn't work
by removing from doctype through the next

!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.=
w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"

Then load it into WM. It should display in quirks mode,
so that if that's the problem then the edited email
will display OK.
I know that different IE versions vary when displaying
in standards mode, but I'm not familiar with the details.
(It's such a mess that I just design all webpages to display
in quirks mode.) I'd be surprised if the two modes could
vary so much as to affect image display, but.... who knows.

Other than that, as I said I haven't really studied
it line by line. It would need to be reformatted to make
it readable and then would require a lot of time to find
the exact differences. But if the problem is not the
display mode in different IE versions then the only other
problem I can imagine is that one version of WM is
simply set to display HTML email as text. I know you said
you checked those settings, and you said that some images
do display, so it's a mysterious dilemma to me.