I've tried running the audio through some monitors and then micing the monitor with a dynamic mic, or condensor if you want some room. Compress it pretty hard too. You could maybe apply a eq too to cut or boost what you want....and then...
Take the reamped track and run it onto a cassette tape. Then play the cassette tape on a boombox, and mic the speaker.
Probably too much. but it will sound vintage.
I thought your after example sounded good already by the way. I love that sound!