After fiddling a bit with some home-made scripts and Aegisub, I managed to create a relatively easy workflow to make lyric videos (needs Linux, command-line, and editing text files, so it's totally for nerds). Anyway, the results are uploaded to Vimeo now:
If anyone is curious about the code or the workflow, I'll happily share (I might write a blog post at some point anyway).
Thanks a bunch to @luka for the idea of using ffmpeg to burn subtitles into the video!