I remember listening to these shows when they first came out - when I was a kid.
My great-grandmother would keep her radio on a news-talk station out of Dallas (WFAA - News-Talk 57) and Mystery Theater would be played at night. On the weekends, they would sometimes play episode after episode all night long.
I recently discovered this website:
https://www.cbsrmt.com/synopsis.html
As an added bonus, many of the programs include the news of the day before the program starts, as well as commercials from that time period.