Can Tomcat be configured to interpret all, or selected, .html files within a given context as JSP? Or, do JSP files have to end with a .jsp extension?

yes you can do that by modifying the web.xml file. You will have to invoke the org.apache.jasper.runtime.JspServlet for all the requests having extension .html. You can do that by changing the Servlet mapping code:
<servlet-mapping>
<servlet-name>
jsp
</servlet-name>
<url>*.html</url>

</servlet-mapping>


And comment out the following block

<mime-mapping>
<extension>
html
</extension>
<mime-type>
text/html
</mime-type>
</mime-mapping>