I found a source that confirms the 1992 or 1993 date: https://people.well.com/user/hlr/vcbook/vcbook7.html

“Two years later [after the first conference in 1990], I was invited back, along with John Barlow […].” “[…] which explains why I was invited to Oita in 1990, and why Barlow, Johansen, and Johnson-Lenz were invited to join me there in 1993.”

While 1992 vs. 1993 is still ambiguous (either 1993 is a typo, or the invitation was two-and-something years later), the text confirms that there was a second HyperNetwork conference in Oita in either 1992 or 1993, and that Barlow was invited to it.

EDIT: Another source: https://www.eff.org/pages/complete-acm-columns-collection

“Will Japan Jack In? For the October, 1992 Electronic Frontier column in Communications of the ACM by John Perry Barlow […] At a conference on globally networked computing in Oita Prefecture in February, I was astonished to hear a number of Japanese corporate officials […] proclaim enthusiastically the potential of the "Hypernetwork"[…].”

This would imply that there was a Hypernetwork-related conference in Oita in February 1992 that Barlow attended.