Curiously, in that Bartitsu stick fighting is a predominantly single-handed method, some of the participants in this CBS Minnesota news item on competitive lightsaber fencing claim a Bartitsu background.
While the rules of competitive lightsaber seem closely comparable to those of kendo combined with HEMA longsword, the French combat sport of canne de combat might, perhaps, make a better model. Because the French method was specifically devised as an “artistic fighting style”, the rules require moulinets and extensions on every attack and award higher points for executing spectacular techniques such as leaps and pirouettes. In that sense, it’s rather closer to the flashy, cinematic style featured in the Star Wars movies.
An adaptation of canne de combat rules to the predominantly two-handed lightsaber would yield a visually unique and competitively challenging new combat sport.