Custom, separate search form and search results page in Wordpress - php

Question

Goal/Information
I'm trying to set up a custom search field and custom search results page to display one category of pages. I need these results on a separate, custom search results page so I can customize how the results are displayed without affecting the default search.
For context, I'm setting up a gallery where the user can search for keywords and relevant pages will be displayed as a thumbnail grid, with each thumbnail linking to a page containing more information on the image.
Each page, containing the image and information, is set up as a page (not post) under the category images.
I'm not sure this is relevant, but in a previous project I've set the default search to exclude images pages with the following code in my functions.php (category ID is 30). I've tried removing this code and it didn't affect my problem described below.
/* Exclude a Category from Search Results */
add_filter( 'pre_get_posts' , 'search_exc_cats' );
function search_exc_cats( $query ) {
if( $query->is_admin )
return $query;
if( $query->is_search ) {
$query->set( 'category__not_in' , array( 30 ) ); // Cat ID
}
return $query;
}
What I've Tried
I'm still learning php and have spent many hours on this to no avail. Most recently I tried tweaking some code from this similar question.
My resultant custom search form looks like this:
<form class="search-form" action="<?php echo home_url( '/' ); ?>" method="get">
<input name="s" type="text" placeholder="Search Images" />
<input name="post_type" type="hidden" value="page" />
<input name="category_name" type="hidden" value="images" />
<input alt="Search" type="submit" value="Search" />
</form>
I've added the following code to the top of my search.php to attempt to redirect to another results page, in this case search-page.php, if the post type has been specified:
<?php
// store the post type from the URL string
$post_type = $_GET['post_type'];
// check to see if there was a post type in the
// URL string and if a results template for that
// post type actually exists
if ( isset( $post_type ) && locate_template( 'search-' . $post_type . '.php' ) ) {
// if so, load that template
get_template_part( 'search', $post_type );
// and then exit out
exit;
}
?>
Note: I took this directly from the similar question linked above.
I've duplicated search.php into search-page.php, removing the code above from the latter.
Problem
Now let's do a search in the custom form above for "marble" (a term featured in one of the image pages). The URL looks right (http://example.com/%3C?s=marble&post_type=page&category_name=images), but I get a 404. In addition, normal searches (those not in the custom form) now take me to a white page – not even a 404. When I remove the above code from functions.php, the default search works properly. (Custom search still 404s.)
Other Attempts
I've also read this guide from Smashing Magazine a few times – Building An Advanced WordPress Search With WP_Query – but can't quite pick out the information relevant to me.
I've tried a couple dozen other guides and questions, but most of them deal with searching for a specific post type alone (and not a category) or searching from a radio-button selection of categories. I haven't been able to scrape any working solutions from them.
Are there any tweaks to what I've tried – or completely different solutions altogether – that will help achieve the desired effect? Specifically, how to create a custom search form for one type of page category, leading to a customizable, separate search results page (independent from the default search results page).
Thanks in advance.