The Travel Editor replies: It is not entirely clear whether you would like a wholly organised group tour or not, but there are a couple of interesting UK operators that could organise such tours.
Andante (tel: 01980 610555) specialises precisely in archaeological and art history tours, and Sicily is included in its programme. These tours are very specialised and led by an expert guide. There is also a 10-day tour taking in Palermo, Segesta, Agrigento, Syracuse, Piazza Armerina, Taormina for pounds 1,540 per person. Another similar operator is Martin Randal (tel: 0181-742 3355) which offers equally specialist 12- day tours for pounds 1,780.
You have already said that this kind of trip seems "ridiculously rushed", though, personally, I don't think it is: Sicily is not a very big place. Anyway, if you want to stay on by yourself at the end of the tour, the operators say that they can easily arrange this. By the way, flights to and from Sicily are via Rome, and stopovers with no extra charge for the flight are also perfectly feasible.
As an alternative to taking a group tour, you could, of course, spend three weeks in Sicily on a fly-drive and take a very good archaeological guidebook (such as a Blue Guide) with you. A delightful example of an operator doing fly-drive farm holidays in Sicily is Sunvil (tel: 0181- 568 4499). It handles Azienda Mose at Agrigento, a huge country house set in grounds beside the so-called Valley of the Temples (one of Sicily's richest archaeological sites). A week's half-board there costs from pounds 590 per week, including flights and car hire. The food and atmosphere will be wonderful.