Crazy idea, but what happens if you record audio and video with different ffmpeg processes?
I also tried that with the -map parameter, if that's what you mean. Same outcome.
Also, you mentioned this works better with other software — any idea if those settings are drastically different than your ffmpeg settings?
SimpleScreenRecorder is very basic, but it works well, except for some random dropped frames here and there. No big deal, but sometimes it's noticeable enough for me to feel uneasy. 1920x1080, 60 fps, PulseAudio, H.264 video codec, ultrafast preset (skipping frames) and vorbis audio codec at 128 kbps. Just that.