I was able to create a work-around that solved for my needs.
I actually deactivated the CF7 datepicker plug-in.
Instead of selecting a field type “date” when I generate my tags I chose “text field” and then gave that text field an ID (in my example the ID is “date”).
Then I added the following script to the page to hook-in the datepicker to the field I had just created
<script>
$(function() {
$( "#date" ).datepicker();
});
</script>
Depending on your theme, you may also need to add some or all of the following to make it work:
<link rel="stylesheet" href="https://code.jquery.com/ui/1.10.3/themes/smoothness/jquery-ui.css" />
<script src="https://code.jquery.com/jquery-1.9.1.js"></script>
<script src="https://code.jquery.com/ui/1.10.3/jquery-ui.js"></script>
<link rel="stylesheet" href="/resources/demos/style.css" />
Obviously, this does not pass the date formatted as an actual date to the database, but I’m guessing for most applications having the date info formatted as a date isn’t necessary.