Writing to bigger files leads to Internal Server Error - php

Question

Implementing a feature for uploading files with a (potentially) unlimited filesize using chunked-file uploading and WebWorkers, I stumbled upon a quite strange problem:
Whenever I try to attempt to write to a file bigger than 128 MB - 134 MB using fwrite(), an internal Server error is raised and, thus, script execution is stopped. The problem could be simplified to this (hopefully self-explanatory) test-case:
$readHandle = fopen("smallFile", "r"); // ~ 2 MB
$writeHandle = fopen("bigFile", "a"); // ~ 134 MB
// First possible way of writing data to the file:
// If the file size of bigFile is at approx. 134 MB, this
// will result in an HTTP 500 Error.
while (!feof($readHandle)){
fwrite($writeHandle, fread($readHandle, 1024 * 1024));
}
// Second way of reproducing the problem:
// Here, the data is just NOT written to the destination
// file, but the script itself doesn't crash.
// stream_copy_to_stream($readHandle, $writeHandle);
fclose($readHandle);
fclose($writeHandle);
When using stream_copy_to_stream, the script doesn't crash, but the data is just not written to the destination file.
Having contacted the support-team of my (shared) server host, I got the answer that this limit had something to do with the php configuration variables post_max_size and upload_max_size. However, neither do the set values (96MB for both) correspond to the measured maximum file size (134MB) at which files are writeable, nor does the problem exist when I apply the same values to my local test server.
Also, I could not find any information about a potential correlation between PHP_MEMORY_LIMIT (the offer I am using states 512MB) and the maximum writeable file size of 128 - 134MB (of which 512MB is a multiple).
Does anybody know if
the said configuration values really correspond to the problem at all?
there is any other way of continuing appending data to such a file?
PS: This SO thread might be based on the same problem, but here the question(s) are different.