Thank you that is very interesting. So at least it is possible that at about the same time Chinese blade forms were making their way to Japan, they also made their way to Aceh. Then such blades largely disappeared in China, evolved into the Katana in Japan, and remained largely unchanged in Tibet and Aceh.
The Chinese blades that made it to Japan at that time often had a medial ridge, and perhaps a faceted tip. I have never seen such on any Tibetan sabers from the last 400 years or so, but there is one 14th-15th century version shown in Warriors of the Himalayas with a medial ridge. The ridge was supposedly lost in China at the time and was reintroduced from Japan at the end of the Ming. Have you ever seen one from Aceh with a ridge? It wouldn't prove anything either way, but it would be interesting.
I don't think there is going to be more than circumstantial evidence either way, but some evidence for a 13th c straight backed saber in Aceh would certainly help
Is there any evidence that people consider the straight-backed saber older or more traditional than the Indian influenced sabers?
Josh