Pagination breaks when page is set to front page?

So I’m noticing some very strange behavior.

Pagination breaks inside my front-page.php on page 3. Instead of page 3, I get thrown onto the index page.

<?php
$args = array(
'post_type' => 'food',
'posts_per_page'=>9,
'paged' => $paged,
); 

$wp_query = new WP_Query( $args );
?>

<?php while ($wp_query->have_posts()) : $wp_query->the_post(); ?>

<?php the_title() ;?>

<?php endwhile; ?>

<?php wp_reset_postdata(); ?>

<?php previous_posts_link('Prev') ?>
<?php next_posts_link('Next') ?>

But when testing this code inside of a normal page template, the pagination works just fine.

Also, a strange quirk that might divulge some more information… For some reason if I change the reading settings to “Blog pages show at most [5]”, the 3rd page seems to work but not the 4th page.