Was a 7300-mile non-stop flight possible in 1979? I'm listening to the On Wings of Eagles audiobook by Ken Follett and found some information about a non-stop transatlantic flight between Teheran (IKA) and Dallas (DFW). GCM says that this is 7,300 miles and Google says that's 11,750 km.

Was there any aircraft capable of performing such a flight in 1979? If yes, then which one?

It was expected to travel with about 10-15 people on board and non-stop flight seems to be essential (at least to the author, because I completely don't understand the reasons why such a flight couldn't take a re-fueling break at some European airport once clear of the dangerous zone of Iran's / Middle East's airspace).

The author's choice of either a Boeing 707 or 727 seems to be completely incorrect, as according to Wikipedia there wasn't any version of either of those aircraft capable of flying 7,300 miles non-stop (or I'm missing something). The longest range mentioned is 10,650 km in the case of the B707-320B.
Even for zero payload, no B707 model is able to fly more than 6000nmi (11111km). B727 even has less range.

However, Iranair planned to run Tehran-LAX flight, which length is 12222km, but never materialized because of 1979 revolution. The flight could have been operated by the 747SP (introduced in 1976), similar to their Tehran-JFK route.