Record all conversations using a device on your person and process them later
Processing and extracting multiple conversations at different levels from a single audio source automatically would be a great project to attack with some quite simple sound engineering tools and speech recognition ML.
1) Microphone all possible tables and have them record/signal when key words are overheard
2) Befriend/seduce/bribe wait staff and train them to roam around in optimal patterns to catch conversation
3) Some kind of subtle hearing amplification/focusing device
4) Record all conversations using a device on your person and process them later