Next round of programming yields:

def panflute_to_bike_etree_nr(e, level=0) -> ET.Element:

    # questions about how header levels are handled as we put them into the etree
    etree = None
    stack = [(e, level)]
    # current ul_elem
    ul_elem = None
    heading_level = 0

    while stack:
        (e, level) = stack.pop()
        print("  " * level, e.tag)

        if is_inline_or_contentless(e):

            li_elem = ET.Element("li")

            # TO DO: handle rich text
            p_elem = ET.SubElement(li_elem, "p")
            p_elem.text = pf.stringify(e).strip()

            # 2 things to figure out: parent_ul (where to attach li_elem) and what the current ul_elem is

            if e.tag == "Header":
                print ("header", e.level, e.identifier, e.classes, e.attributes, pf.stringify(e))
                li_elem.attrib["data-type"] = "heading"
                li_elem.attrib["data-level"] = str(e.level)

                if e.level > heading_level:
                    # child
                    parent_ul = ul_elem
                    print ("e.level > heading_level", ul_elem)
                elif e.level == heading_level:
                    # sibling
                    # parent_ul has to be ul parent of ul_elem                    
                    parent_ul = ul_elem.getparent().getparent()
                else:
                    # e.level < heading_level
                    # uncle or higher
                    parent_ul = find_ul_ancestor(ul_elem, int(e.level)-1)

                heading_level = e.level
                ul_elem = ET.SubElement(li_elem, "ul")
                parent_ul.append(li_elem)
            else:
                ul_elem.append(li_elem)

        else:
            if e.tag == "Doc":
                etree = empty_bike_etree()
                ul_elem = etree.xpath("//ul")[0]
            else:
                # BulletList
                # OrderedList
                # ListItem
                print("block", e.tag)

            try:
                for c in reversed(e.content):
                    stack.append((c, level + 1))
            except AttributeError:
                pass

    # clean up etree by adding ids
    etree = add_ids_to_bike_etree(etree)
    return etree