I run a Multi-Site WP installation very successful since many years on FreeBSD+Apache+PHP56. Some time ago I encountered the same problem with file uploads. More specifically:
*) image upload works
*) uploading files with disallowed extensions fails (as expected)
*) uploading allowed file types other than images, e.g. mp3 fails with “HTTP error”
I tried all those options shown within this thread without success. The Web server log shows that the child process of the Apache segfaults. When I decrease PHP memory_limit the log file shows the error message of memory_limit and segfaults immediately afterwards. When increasing the memory_limit again the mem_limit-error-message goes away but it keeps segfaulting. I re-istalled all binaries without any success.
The problem was solved after upgrading PHP from 5.6 to 7.2.