To many long running Apache processes in READ status without requests after a certain time
Problem solved.
The solution was to lower the Apache's Timeout value to a number like 15. As I realized for running a long PHP script (even for hours) do not need to this timeout to be hight, it's enought that the PHP's max_execution_time to be big enought.
Update
I have also upgraded to PHP 7.1 with FastCGI under PHP-FPM, and I have changed the Apache's MPM mode to event as esra-s suggested, and it runs like hell. Many thanks!