How can I fix a slow redirect after form submit from frontend (no plugin)?

Question

Below is the code I'm using for my short-coded form and to add the post.

Here's a basic overview of the problem I'm trying to remedy:

-This form is displayed on the page at /addmember/ -On this page is also a list of existing members, current and pending (members being a custom post type)

-This form is used to submit what will be a pending member

-On submit of this form the member is automatically given a pending status and would be then displayed in the pending members section of the /addmember/ page -So the idea is then that after the member is submitted the page is refreshed to show the new pending member in the pending member list on the /addmember/ page

-Right now this is functional BUT after a user clicks submit, the /addmember/ page appears to refresh--all the user sees is that same form with empty fields--the lists do not appear, no other information on the /addmember/ page appears. All they see is that empty form. -Then finally after a few seconds the are redirected to/the /addmember/ page refreshes

***I want to figure out a way to eliminate that odd moment when they see that almost empty page with just the empty form before it finally redirects/refreshes. How can I do this? I've tried using wp_redirect instead but that seems to have no effect. And I can't move the refresh action up any farther in the code.

<?php    
function ty_front_end_form() { ?>

            <form id="mreg" method="POST" action="">

            <label for="mfname">Name</label>
            <input type="text" id="mfname" name="mfname" value="" /><br/>

            <label for="mem">Email</label>
            <input type="text" id="mem" name="mem" value="" /><br/>

            <label for="mpw">Why</label>
            <textarea id="mpw" cols="19" rows="4" name="mpw"/></textarea><br/>

            <input type="submit" name="submit" value="Submit" style="margin-left: 201px; background: #000;"/>   

            <input type="hidden" name="second-nom" id="second-nom" value="No" />            
            <input type="hidden" name="start" id="start" value="1" />           
            <input type="hidden" name="post-type" id="post-type" value="add-members" /> 
            <input type="hidden" name="action" value="add-members" /> 

            </form>
            <?php

            if( isset( $_POST['start'] ) ) {
                ty_save_post_data();
            } ?>


<?php }

        add_shortcode('add-members','ty_front_end_form');


        function ty_save_post_data() {


        $post = array(
        'post_title' => $_POST[ 'mfname' ],
        'post_status' => 'publish', 
        'post_type' => 'add-members' 
        );  


        $post_id = wp_insert_post($post); 

        add_post_meta($post_id, 'mfname', sanitize_text_field( $_POST[ 'mfname' ] ), true);
        add_post_meta($post_id, 'mem', sanitize_text_field( $_POST[ 'mem' ] ), true);
        add_post_meta($post_id, 'mpw', esc_attr( $_POST['mpw'] ), true);
        add_post_meta($post_id, 'second-nom', sanitize_text_field( $_POST[ 'second-nom' ] ), true );
        $location = 'http://example.com/addmember/';  
        echo "<meta http-equiv='refresh' content='0;url=$location' />"; 
        exit;
        } 

?>

PER MILO'S ANSWER HERE IS THE UPDATED CODE

<?php    
function ty_front_end_form() { ?>

            <form id="mreg" method="POST" action="">

            <label for="mfname">Name</label>
            <input type="text" id="mfname" name="mfname" value="" /><br/>

            <label for="mem">Email</label>
            <input type="text" id="mem" name="mem" value="" /><br/>

            <label for="mpw">Why</label>
            <textarea id="mpw" cols="19" rows="4" name="mpw"/></textarea><br/>

            <input type="submit" name="submit" value="Submit" style="margin-left: 201px; background: #000;"/>   

            <input type="hidden" name="second-nom" id="second-nom" value="No" />            
            <input type="hidden" name="start" id="start" value="1" />           
            <input type="hidden" name="post-type" id="post-type" value="add-members" /> 
            <input type="hidden" name="action" value="add-members" /> 

            </form>


<?php }

        add_shortcode('add-members','ty_front_end_form');


        function ty_save_post_data() {

        if( isset( $_POST['start'] ) ) { 

            $post = array(
            'post_title' => $_POST[ 'mfname' ],
            'post_status' => 'publish', 
            'post_type' => 'add-members' 
            );  


            $post_id = wp_insert_post($post); 

            add_post_meta($post_id, 'mfname', sanitize_text_field( $_POST[ 'mfname' ] ), true);
            add_post_meta($post_id, 'mem', sanitize_text_field( $_POST[ 'mem' ] ), true);
            add_post_meta($post_id, 'mpw', esc_attr( $_POST['mpw'] ), true);
            add_post_meta($post_id, 'second-nom', sanitize_text_field( $_POST[ 'second-nom' ] ), true );
        } 
        }

add_action( 'init', 'ty_save_post_data' );

?>

Answer 1

Hook your form processing code to an action that runs before the page is rendered and no redirect will be necessary.

function wpd_check_submission(){
    if( isset( $_POST['start'] ) ) {
        // do your post insertion here
    }
}
add_action( 'init', 'wpd_check_submission' );