The problem was solved by listing the jCarousel .js libraries AFTER the Angular libraries in the HEAD. Here's an example that shows both Angular populated and manually populated carousels working correctly:
<script type='text/javascript' src='//cdnjs.cloudflare.com/ajax/libs/angular.js/1.2.1/angular.js'></script>
<script type='text/javascript' src='//cdn.jsdelivr.net/jcarousel/0.3rc1/jquery.jcarousel.min.js'></script>