OK, well, I don’t know what you’ve done to modify the pdb-list-detailed.php template, so I can’t say what the problem is. That is the place to start, so you were on the right track and I thought you would figure it out.
Anyway, a good way to get more control over the search UI is to look a the HTML generated by the plugin for a working search control. You can simply copy the HTML contained within the fieldset tags and then use that HTML in the template instead of the functions that generate the search UI, so you end up with this: (this is a fragment of the detailed template in which I have replaced part of the search form with the literal HTML from the web page.)
<?php $this->search_sort_form_top(); ?>
<?php if ( $filter_mode == 'filter' || $filter_mode == 'both' ) : ?>
<fieldset class="widefat inline-controls">
<legend>Search:</legend>
<select id="search_field_select" name="search_field" class="search-item">
<option value="none">(select)</option>
<option value="first_name">First Name</option>
<option value="last_name">Last Name</option>
</select>
<input name="operator" type="hidden" class="search-item" value="LIKE">
<input id="participant_search_term" type="text" name="value" class="search-item" value="">
<input name="submit_button" type="submit" value="Search">
<input name="submit_button" type="submit" value="Clear">
</fieldset>
<?php endif ?>
So, that is just an example, but the idea is now you can easily set the default selection for the dropdown and add a placeholder to your text input. It’s not as flexible, you have to manually add all your dropdown values, but it’s easy to see how to modify the form for your purposes.