I have it working now; here's what I discovered from poking around 14 hive.
First, you need to create a layouts.sitemap.*.xml file that lists your additions to the site structure, and deploy it to the LAYOUTS directory. If you look in the LAYOUTS you'll see a bunch of these files in there which you can use as examples. For a page that hangs off the List Settings screen it should look something like this:
<?xml version="1.0" encoding="utf-8" ?>
<siteMap enableLocalization="true">
<siteMapNode url="/_layouts/MySettingsPage.aspx?List=1" parentUrl="/_layouts/listedit.aspx" title="My Settings" requiredParameters="List" />
</siteMap>
Note that you'll need to copyappbincontent on each front-end server to get your pages merged into the main sitemap.
Even though your page is listed in the sitemap, SharePoint will still pretend it doesn't know about it until you wire things up on the page itself.
<asp:Content ContentPlaceHolderId="PlaceHolderPageTitleInTitleArea" runat="server">
<a href="<%= SPHttpUtility.UrlPathEncode(list.DefaultViewUrl, true) %>">
<% SPHttpUtility.HtmlEncode(list.Title, Response.Output); %>
</a>
<SharePoint:ClusteredDirectionalSeparatorArrow runat="server" />
<a href="<%= SPHttpUtility.UrlPathEncode("listedit.aspx?List={" + list.ID.ToString() + "}", true) %>">
<SharePoint:FormattedStringWithListType runat="server" String="<%$Resources:wss,listsettings_titleintitlearea%>" LowerCase="false" />
</a>
<SharePoint:ClusteredDirectionalSeparatorArrow runat="server" />
<SharePoint:EncodedLiteral runat="server" text="My Settings Page" EncodeMethod='HtmlEncode'/>
</asp:Content>
<asp:Content contentplaceholderid="PlaceHolderTitleBreadcrumb" runat="server">
<SharePoint:ListSiteMapPath
runat="server"
SiteMapProviders="SPSiteMapProvider,SPXmlContentMapProvider"
RenderCurrentNodeAsLink="false"
PathSeparator=""
CssClass="s4-breadcrumb"
NodeStyle-CssClass="s4-breadcrumbNode"
CurrentNodeStyle-CssClass="s4-breadcrumbCurrentNode"
RootNodeStyle-CssClass="s4-breadcrumbRootNode"
HideInteriorRootNodes="true"
SkipLinkText="" />
</asp:Content>
This seems like a lot of work. I can't help but think that there ought to be a standard SharePoint "breadcrumb" control that leverages the sitemap and provides standard behavior and formatting. But this is how Microsoft's own pages seem to do it.
Hope this helps someone!