Hi Karlis,
The problem is that the browser is trying to load the entire video in a single HTTP request which will not work for such large files.
To fix this In addition to the content-type header, videos need more headers to allow for buffering, scrubbing etc.
Specifically, you need to check the content-range and content-length headers in the incoming request and serve the appropriate bytes. The response should contain the same headers.
For more details see https://ianmcdowell.net/projects/http-mp4-streaming/
Some example code on how to do this with Java https://gist.github.com/fehmicansaglam/1781977
Hope this helps
Contact Menno de Haas on Slack. I know he built a small module/java action to support streaming objects. Maybe he can publish it for you in the appstore