So, how does one get around this unfortunate problem?  Well, the best method I’ve found is to set the innerHTML property when the element is not yet attached to the DOM or is attached in a “safe” place (usually at the BODY tag).  To make this process simpler, I generalized this into a function that creates a new DOM node of the same type, preserves any attributes I care about, sets the innerHTML property, and replaces the original node in the DOM with this new node having the desired innerHTML.  Here’s the function for reference:

function replace_html(el, html) {
	if( el ) {
                var oldEl = (typeof el === "string" ? document.getElementById(el) : el);
                var newEl = document.createElement(oldEl.nodeName);

                // Preserve any properties we care about (id and class in this example)
                newEl.id = oldEl.id;
                newEl.className = oldEl.className;

                //set the new HTML and insert back into the DOM
                newEl.innerHTML = html;
                if(oldEl.parentNode)
        	        oldEl.parentNode.replaceChild(newEl, oldEl);
                else
		        oldEl.innerHTML = html;

                //return a reference to the new element in case we need it
                return newEl;
	}
};

Hopefully this function will help someone out there work around this problem a little faster than I originally did.