Actually, <BR/> would be the start of a SHORTTAG construct (ending with the next slash).

"Actually"? Not only do I know that, I covered that case. ("Browsers don't support the correct use.")

but it's a valid SGML construct, and the HTML DTD doesn't prohibit it (unfortunally)

Not quite. BR can't have a body. <BR// might be valid HTML, but <BR/<.../ is not.