12 years later, Word-HTML still use lots of  's for formatting list-items. Worse, those  's tend to be specified incorrectly. Consequently, Word-HTML's lists often have incorrect and inconsistent indentation.
I recently wrote a Python program that fixes these problems in Word-HTML, for bulleted and ordered-lists. The program is part of the open-source system WordWebNav (WWN).
In Word-HTML, each list-item is an HTML paragraph (<p>). WWN fixes the Word-HTML lists by correcting those HTML paragraphs, e.g., it ensures the correct number of  's are used. This seemed simpler than replacing HTML paragraphs with HTML list-items (<li>), as proposed in the OP.
Most of the Word-HTML parsing is too complex for regex
WWN uses BeautifulSoup to do the bulk of the HTML parsing and editing. This avoids the known problems from using regex to parse HTML. Those regex problems are described in other answers to the OP, and here.
Fixing the Word-HTML lists involved researching Word-HTML files, to discover the various ways incorrect HTML is generated. BeautifulSoup was used to parse and fix the buggy Word-HTML. There's a lot of variation in the Word-HTML for lists, and parsing that HTML with regex's would be especially problematic. For example, the HTML paragraph-tags (<p>) can contain randomly-placed span-tags with a "lang" attribute:
<span lang=EN-GB>...</span>
WWN uses regex for some HTML parsing, but it's only for small subsets of the HTML, where there's little variation in the content.
The Word-HTML research-results, and the parsing-code are too complex to fully describe here. Highlights are described below.
Word-HTML's bugs, that cause mis-formatted lists
For list-items, Word-HTML uses  's to set the indentation before the list-symbol (e.g., number).  's are also used to set the spacing between the list-symbol and the start of the list-item's text. The number of  's used is often incorrect and inconsistent. The problem is the worst with multi-level lists. WordWebNav's docs show examples.
With ordered lists, another cause for mis-formatted list-items is using incorrect values for the style attribute "text-indent". This affects the spacing before the list-symbol.
Example Word-HTML, for mis-formatted list-items
A bulleted-list list-item, with lots of  's after the bullet-symbol ("·"):
<p class=MsoListParagraphCxSpFirst style='margin-left:.25in;text-indent:-.25in'><span
style='font-family:Symbol'>·<span style='font:7.0pt "Times New Roman"'>
</span></span>This is the list-item's text.</p>
An ordered-list list-item, with  's before and after the list-symbol ("i."):
<p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;text-indent:-1.5in'><span
style='font:7.0pt "Times New Roman"'>
</span>i.<span style='font:7.0pt "Times New Roman"'>
</span>This is the list-item's text.</p>
Bullet symbols that don't display properly in Firefox
For bulleted-lists, there are two list symbols that don't display properly in Firefox. They are shown in the WordWebNav doc's examples, cited earlier.
Using BeautifulSoup to fix the Word-HTML bugs in lists
WWN has a program create_web_page.py, and it fixes the bugs in the Word-HTML lists. The program also fixes other bugs in Word-HTML, and it adds features to the Word-HTML, to make it a more usable web-page (e.g., a Navigation Pane is added).
The code in create_web_page.py is commented, and it explains the parsing and fixes for the HTML bugs. The code-sections that process lists are identified by block comments, e.g.,
'''
######################
Code Section: Fix the list-items in ordered-lists
######################
'''