I've found a way to eliminate the 'Recent Posts' element from the twentyeleven Showcase template. There's a section in showcase-template.php marked '<section class="recent-posts">.' In my Dreamweaver it starts on line 159.
Delete everything from '<section class="recent-posts">' to the end, '</section>,' line 212. I renamed the file 'New Showcase Template.'
Here's the result: http://www.cartoonscripts.com/blog/.
The problem I haven't solved is that the content margins narrow to the Default. I edited style.css to change references '.page-template-showcase-php' to '.page-template-new-showcase-php' but it didn't work. Just in case I saved the original style sheet as 'old-style.css.'