Nanyuan Luohan Shiba Shou
I had my previous suspicion confirmed by my shishu (who is currently in Shaolin bringing back some material at the request of the monastery) regarding the identity of this style. It is indeed the Kanjiaquan of Nanyuan Tongbeiquan (btw, he uses the bei character for this, but bi for the Renshou Tongbiquan showing they are also from different periods/origins as I suspected).
The old name in the local tradition is Xiaosihui (4 small rounds), which is four shoufa in one huihe (round), four rounds in total. It was later just called Luohan Shiba Shou because it has 18 postures. So it is just by namesake.
However, there is only this one set. The others in the encyclopedia are from external sources that have the same name, so they were lumped together. Hence, only the first set in the 8 is like Nanyuan Tongbeiquan.
But still, the others I find are similar to Renshou Tongbiquan and the 13 Kanjiaquan sets, but they are not from the same source. Renshou Tongbiquan is also part of Shi Zhenxu's heritage, but not these other roads of Luohan Shiba Shou. So, I assume they must be from the same line as the 13 road Kanjiaquan system from Shi Sufa, shown by Shi Dejun. They are in fact much more similar to that than to Renshou Tongbiquan.