How to initiate a file download after Gravity Forms AJAX submit

I have a Gravity Form where users have checkboxes set up to choose which files to download. For enhanced UX, the form is multi-page and uses AJAX. Using the following PHP function and Gravity Forms Hook, I am able to loop through the selected checkboxes and add files into a ZIP Archive, but can't currently start the download.

add_filter( 'gform_after_submission_3', 'download_brochures_message', 10, 4 ); function download_brochures_message( $entry ) < $confirmation = "Your download should begin shortly. \r\n"; $error = "Files not set \r\n"; $file1 = rgar( $entry, '1.1' ); $file2 = rgar( $entry, '1.2' ); $file3 = rgar( $entry, '1.3' ); $file4 = rgar( $entry, '1.4' ); $files = array( $file1, $file2, $file3, $file4 ); print_r($files); $zip = new ZipArchive(); $current_time = time(); $file_folder = wp_upload_dir(); $dir = $file_folder['path']; $zip_file = tempnam( $dir, time() ); $zip->open( $zip_file, ZipArchive::CREATE ); foreach ($files as $file) < $zip->addFile($file); > $zip->close(); echo $zip_file; header('Content-disposition: attachment; filename="'.$zip_name.'"'); header('Content-type: application/zip'); header('Content-Length: ' . filesize($zip_file)); header("Location: $zip_file"); readfile($zip_file); > 

Since the form submit's via AJAX, the page headers have already been sent and the PHP errors I receive are "Cannot modify header information - headers already sent". How could I modify this code to allow the zip to download?