I took a closer look at that theme, the preview boxes limit the amount of information displayed, which is cutting out any code that PowerPress adds. The only other option you have is to add the following code within the theme where you want the player and links added by PowerPress to be inserted. Here's the code you would add to your theme.
<?php if( function_exists('the_powerpress_content') ) the_powerpress_content(); ?>
I can't confirm this will work because I do not have the theme installed, but I believe the following steps will work.
Edit home.php in the structure theme. Where you see the following...
<div class="entry-summary">
<?php the_excerpt(); ?>
</div>
Add the line I mentioned:
<div class="entry-summary">
<?php if( function_exists('the_powerpress_content') ) the_powerpress_content(); ?>
<?php the_excerpt(); ?>
</div>
Once you do this, go into PowerPress Settings under the Appearance Tab and uncheck the option to include the player in excerpts.
You will still need either the plugin or the try to fix setting enabled as first mentioned as well as these steps to get the player to appear in your home pages.
One other thing you can try
One last shot in the dark, you could try setting the priority level PowerPress uses to something very high. To do this, you need to be able to edit your wp-config.php file in the root folder of your blog. Add the following line near the top. The line must be added before the require() line near the bottom of the file or else it will not work.
define('POWERPRESS_CONTENT_ACTION_PRIORITY', 1000 );