How to properly play 720p/1080p media with subtitles through MHL (HDMI out)?
If you're rooted you could try to force a certain combination of phone screen resolution and DPI using Second Screen and maybe your selected video player will conform to that even as the video is being streamed out through MHL.

Just make sure you keep failsafe options like "don't keep settings after restart" enabled in case your experimental Second Screen settings make your screen unusable.