Hi Mike,
The logo uploader just using the WP Media Library which will set the protocol to whatever WP has set.
One alternative is to use GP Hooks to show your logo instead. First you would remove it from the Customizer, and then add this into the “Before Header Content” hook:
<div class="site-logo">
<a href="URL TO YOUR HOMEPAGE" title="YOUR SITE TITLE" rel="home">
<img class="header-image" src="HTTPS URL TO YOUR LOGO" alt="YOUR SITE TITLE" title="YOUR SITE TITLE" />
</a>
</div>