As I understand it, and I'm not an expert in the field by any means, Nakayama Hakudo studied with Uchida Ryogoro who went to Tokyo before Shimizu Takaji did by many years. (Earlier generation, you'll find an annoted lineage here
http://ejmas.com/jnc/jncart_taylor_0900.htm)
The last years of Nakayama's teaching life were spent in the dojo of Danzaki Tomoaki, and the folks in that dojo, according to one of my sensei who studied iai there for several years, also practiced jodo. He wouldn't know if it was "mainline" or "modified" but I suspect it was likely what was taught there by Nakayama.
According to Matsui Kenji (you can get a ref. to that book at the link above) the jodo practiced by Nakayama's group was slightly different than that practiced now.
Just speculation on my part but I'd doubt that Nakayama wanted to improve or change anything he was taught. I suspect he taught as he was taught and as he remembered. He traveled from Tokyo to Kochi to learn iai, and he learned jodo from a fellow who had left Fukuoka a generation before Shimizu and Otofuji started teaching, so I would expect that his iai and his jodo would be different than what ended up as "mainstream", hence his MJER became MSR and his jodo may be different (I'll take Matsui's word on that, he would know) but I doubt he himself ever claimed to be creating anything different. The fact that Nakayama introduced Shimizu to the Tokyo police force also seems to argue against any desire by Nakayama to improve jodo, one would hardly be improving on an art and introduce an exponant of the old ways to the local police force as a teacher of that art.
Looking back at that article I am surprised I claimed that Shiriashi Hanjiro was the sole instructor through the Meiji period, I've just said that his contemporary Uchida was teaching in Tokyo at the same time, and that teaching came down to this day at least in Nakayama's dojo. I suppose I was speaking in terms of the "headmaster lineage" and Uchida was not included in that lineage.
If this is an important question you could write to Matsui and ask, or check with someone in the Danzaki dojo, I would assume it's still going although Danzaki s. has died. You could also ask Mitsuzuka Takeshi who studied with Nakayama as well and who, I believe, used to teach jodo in the States although I think the San Shin Kai in the US is now strictly iaido.
Kim Taylor