Yes! The beta version linked above seems to have fixed the issue. At least two shorter sequences exported breezily to flawless MP4s. (H264) I'm exporting the main sequence just now.
Thousand thanks!
Edit: I was little bit hasty to celebrate. Still the whole project didn't export, but created corrupted video file. However now all other sequences exported to MP4 without issues, and I could join these files together with a new sequence.
Also checked, this beta is version 7.34, previous was 7.33.
Sidenote: I tested other file formats and codecs, and WEBM (VP8) seemed to be only one which created acceptable quality with reasonable file size. But encoding was ridicilously slow, my ten minute project took several hours to export. And of course this might represent a needles decoding-encoding step.