Downloading large files

I'm looking reliable and memory-friendly solution for downloading large files through webpage. And I mean large (video) files like 5-15GB or even larger and files are mainly located on same server with webpage. I'm using shared hosting.

I would use HTML5 download which usually haven't failed me, but this time I need that file exact location will remain unknown for client.

So I have been testing out header solutions like this one and update part of this one. With both my Cpanel showed physical memory usage 100% (1.5GB) and downloads died before download progress reached to 2GB (download speed just dropped to 0), file was 4.8GB.