An API is just an API. As long as the API is the same it doesn't
matter what program is presenting it. I think you missed the part
where I wrote "emulator". APIs can be emulated. Take
http://www.iol.ie/~locka/mozilla/control.htm for instance: it presents
the same API as IE but with the Gecko engine (or at least as much of
the API as it can or needs to present.)
I'm hoping a program exists that can look like Outlook to programs
trying to use its API, but just relay outgoing email to our SMTP
server. It should also preferably be free.

Heck, I'm thinking of
tackling programming it myself as a learning exercise, but I'm sure
that would take too long to suit our present needs.
The program we're wrestling with, BTW is Dydacomp's MOM. The only
email settings it presents are a checkbox to send notices by email,
and a suboption to use Outlook 2000 or later. The documentation only
mentions sending email via Outlook, so I assume the suboption is only
referring to the version or Outlook. I have read elsewhere that it can
use Outlook Express if you have it set as your default email program,
which we don't really want. I tried it with Forte Agent as the default
email program, but it did not do a thing. I have emailed Dydacomp
about it, but figured I'd look into an Outlook-SMTP relay as well and
see what bore fruit first.