I found next workaround. You may escape the redirection after processing POST request by manipulating history object. 
So you have the HTML form:
<form method=POST action='/process.php'>
 <input type=submit value=OK>
</form>
When you process this form on your server you instead of redirecting user to /the/result/page by setting up the Location header like this:
$cat process.php
<?php 
     process POST data here
     ... 
     header('Location: /the/result/page');
     exit();
?>

After processing POSTed data you render small <script> and the result /the/result/page
<?php 
     process POST data here
     render the <script>         // see below
     render `/the/result/page`   // OK
?>
The <script> you should render:
<script>
    window.onload = function() {
        history.replaceState("", "", "/the/result/page");
    }
</script>
The result is:

as you can see the form data is POSTed to process.php script.
This script process POSTed data and rendering /the/result/page at once with:
- no redirection
- no rePOSTdata when you refresh page (F5)
- no rePOSTwhen you navigate to previous/next page through the browser history
UPD
As another solution I ask feature request the Mozilla FireFox team to allow users to setup NextPage header which will work like Location header and make post/redirect/get pattern obsolete.
In short. When server process form POST data successfully it:
- Setup NextPageheader instead ofLocation
- Render the result of processing POSTform data as it would render forGETrequest inpost/redirect/getpattern
The browser in turn when see the NextPage header:
- Adjust window.locationwithNextPagevalue
- When user refresh the page the browser will negotiate GETrequest toNextPageinstead of rePOSTform data
I think this would be excelent if implemented, would not? =)