What is the best method for converting MS Word templates to OTT templates? Specifically, I want to convert templates in .docx format that include tables and pull-down menus with minimal loss of the original formatting and functionality.
Be aware that sometimes it is better to create a new document:
https://forum.openoffice.org/en/forum/viewtopic.php?f=71&t=83694
https://forum.openoffice.org/en/forum/viewtopic.php?f=74&t=4542
Trial and error is what you are searching… 
Using DOTs, or Converting a DOT to OTT, will not only make the conversion artifacts pollute a single document, but generate tons of such documents polluted from their birth. If you need similar templates, please seriously consider re-creating them anew in Writer instead, however extra work it required; it will pay in long run.