Suppress session_start() Warnings (headers already sent) - php

Question

I have a situation where I need to call session_start() in the middle of the file multiple times. Obviously, as session_start() outputs buffer, I get the following warnings:
Warning: session_start(): Cannot send session cookie - headers already sent by...
Warning: session_start(): Cannot send session cache limiter - headers already sent...
There was a lot of written on StackOverflow about header related warnings caused by session_start(). Now before you decide to mark this post as a duplicate, please continue reading - you will see, it is different.
Most of the proposed solutions in the other threads recommend putting session_start() at the beginning of the file, before any PHP output is made. This can be suitable solution if session_start() needs to be called only once per file - however, it is not my case.
I have a file download script (see the code below.) My script regularly, during the file download, updates '$_SESSION' variables with download progress status. I have then another script regularly issued through AJAX requests, which monitors download progress and informs my JavaScript code.
To avoid locking the $_SESSION variables, I therefore have to call session_start() and session_write_close() multiple times per file download, which occurs in a loop in the PHP file.
As every subsequent call to session_start() returns the warnings, which in my case are injected into the downloaded file, is there any programmatically correct way of suppressing them?
Two solutions come to my mind now, but I am not happy with none of them:
calling #session_start() instead of session_start() - this is not considered as a good practice, as it suppresses all warnings and errors returned by the function.
calling ob_clean() to empty the output buffer at the end of every file write iteration, to remove the warnings injected into the buffer to be written to the file. - in this case, the warnings are still present, I do not correctly manage the situation, I simply erase the warning and ignore it.
So my question, please, how to correctly call session_start() and session_write_close() multiple times per file and avoid getting warnings?
Code Sample:
<?php
//...
// file download in small pieces
while(!feof($file_source))
{
$chunk_data = fread($file_source, $chunk_size);
print($chunk_data);
ob_flush();
flush();
$bytes_already_transferred += strlen($chunk_data);
$percent_complete = round(($bytes_already_transferred / $file_size) * 100);
// update session variable, but how to avoid warnings?
if (session_status() == PHP_SESSION_NONE) session_start();
$_SESSION['DownloadProgress'] = $percent_complete;
session_write_close();
usleep(1000);
}
fclose($file_source);
?>