Hi Mike,
What actually fixed the problem was your suggestion (below) that I go to Extensions > Templates > Velocity > Velocity-Default > General, where I put in the full https://... address, and that caused all the stylesheets to load properly. All that was left was for me to add the "https://" to each of the YouTube links in the site, so that they would also display.
"...Also, under the general tab in the configuration you can try supplying a full URL to your site under the setting "Your Site URL if SEO enabled", that will force a url for the css files to use as well."
Thanks so much for your help!
Charlie