Thanks to the advice I got from this forum, I've made some major headway on this issue. (Thank you, Vivek Karandikar!) I enabled the MFC executable as an extension and listed IE 4 as the primary extension for it. Silk now sees the embedded browser as a BrowserChild. That's the good news.

The bad news is that all Silk sees in the browser is HTMLText, HTMLHeadings, and a couple of HTMLPopupLists, when there are lots of HTMLTextFields, HTMLPushButtons, and more. And even though it sees the PopupLists, I can't Get or Select any items listed.

Here are the basic declarations I'm working with:
window MainWin DUCE
__multitag "*Duce"
__DialogBox DUCEDialog
____tag "$59648*"
window BrowserChild EmbeddedIE
__tag "Test Script"
__parent DUCE.DUCEDialog
__HtmlHeading ConfigurationFor
__HtmlHeading Connection
[It's odd that the BrowserChild's parent is a DialogBox within the MainWin, but it works.]
I'm thinking the problem is that there is no defined Browser (with title, status bar, URL, etc.) and what I've got is an 'orphan' BrowserChild.
Any ideas of what's happening and how to work with it?