I regularly frequent Tunis for work and fly on BA. A turnaround is NOT possible. Border Control waiting time can be in excesses of one hour. Also the BA check-in desks (operated by Tunisair) close 40 minutes prior to scheduled departure time.

Also, you are not allowed to PYOBP on the return flight (however you are able to check-in).

I would suggest staying one night in Tunis at an hotel in the city (only about 5 minutes away, and a cab is about 10 Dinars (or about 3 pounds(not on a UK keyboard at the moment)) to the city centre. Hotels can be about 25-40 pounds. They do have some nice Roman ruins in Carthage. But be aware the city is unforgiving if you don't know French or Arabic.

Hope this helps,

BA0197