Canon-wise, Tukayyid is a bit of a mess. Either that, or Clan Smoke Jaguar had about 5 Khans during the Battle of Tukayyid, some who took over after others died, and then gave up their position when the dead men came back. I once read every Smoke Jaguar source, took some notes, and then went crosseyed at all the contradictions.
Well, it's not a mess now. At least, not after
ER:3052. The correct order is:
Khan Leo Showers (3029-3048) *elected ilKhan*
Khan Lincoln Osis (3048-3052) *was either a Star Captain or Star Colonel in the 6th Jaguar Dragoons at the time; when Showers was elected ilKhan, Osis challenged and defeated saKhan Sarah Weaver for the position of senior Khan*
Khan Brandon Howell (3052) *elected as a replacement for Osis; stepped down from Khan's post to become a saKhan when Osis returned from the dead*
Khan Lincoln Osis (3052-3060)
saKhan Sarah Weaver (30??-3050)
saKhan Kincaid Furey (3050-3051) *defeated Weaver for the position after Showers' death*
saKhan Sarah Weaver (3051-3052) *defeated Furey for the position in late 3051; killed on Tukkayid*
saKhan Brandon Howell (3052-3060) *stepped down from Khan's post to become a saKhan*
As for Edmund Hoyt and Dorian Wirth, none of them were Khans. The former one was Loremaster of the Clan and the latter was a Galaxy Commander and Jaguar senior military officer on Luthien.