There is no doubt of the accuracy of Nichiren Daishonin's and Shakyamuni Buddha's recount of the current events of his time by Andinio

We can, of course, disagree on the importance or ideas behind the Rissho Ankoku Ron (Establishing the Correct Teaching for the Peace of the Land). We can agree that independent English-language scholarship about it is slim.

You are correct, there are no historical records about Nichiren besides his own writings. However, according to Habito & Stone, 1999:

Over the course of his career, Nichiren wrote voluminously; his extant corpus contains 498 writings, including both doctrinal essays and letters to his followers, as well as 66 charts, outlines, and extracts, to say nothing of several hundred additional holographic fragments. Of the 498 writings, an astonishing 115 works survive in Nichiren's handwriting, and another 25, destroyed in a fire at the Nichirensha head temple on Mt. Minobu in 1875, are known to have existed.

There are, of course, other examples of historical figures who do not appear in the annals of their times. The historical Jesus has been meticulously constructed based on the New Testament accounts and scant evidence after Jesus's death. From the standpoint of historicity, Nichiren's letters exist. Historians and religious scholars have studied and debated their meaning for centuries.

There are also reliable sources about the natural disasters and epidemics of that era preceding "On Establishing." The Brittanica Encyclopedia article on Nichiren was written by Pier Paolo del Campana, Emeritus Professor of Comparative Religion, Sophia University, Tokyo, a Jesuit-founded university. He states:

The country was at the time afflicted by epidemics, earthquakes, and internal strife.

Jacqueline Stone of Princeton University in Rebuking the Enemies of the Lotus: Nichirenist Exclusivism in Historical Perspective points to "the collective sufferings [Nichiren] saw around him—hunger, epidemics, the great earthquake of 1258 that leveled much of Kamakura, and especially the impending Mongol invasion."

There were unique political, cultural, and geographic circumstances that makes it difficult to trace the spread of disease in pre-medieval and medieval Japan. You are also correct in describing the horrific 753-757 smallpox episode that debilitated Japan. In fact, this episode continued over the centuries in cycles of approximately 10 years. (See: "Smallpox and the Epidemiological Heritage of Modern Japan: Towards a Total History" by Akihito Suzuki.

Epidemiologists have described the years between 1050 and 1260 as "transitional". During these years Japan was continually pounded by small pox, measles, influenza, mumps, and dysentary. However, with continued exposure to these diseases the adult population gradually obtained a degree of immunity although children were still at risk.

According to Nichiren's account he researched and wrote Establishing the Correct Teaching for the Peace of the Land between 1258 and 1260. What was occurring immediately antecedent that prompted him to undertake this project?

The Azuma Kagami chronicles the history of the Kamakura Shogunate from 1180-1266. We do know from this text that in 1256 there was a measles outbreak in the western provinces and it spread the following year to Kamakura. Regent Hojo Tokiyori lost his daughter as well as many other prominent clansmen in this epidemic. He himself fell ill to the disease, lost consciousness, and "miraculously" recovered. It is said that this experience prompted him to retire as regent although he continued to serve as the de facto leader of Japan. [See the dissertation by Roy Ron 2003 (uhm_phd_4313_r.pdf) for more information, pp. 235-236.]

We know that there was a major epidemic in 1257 that caused the authorities to close the Shokan era, 1257-1259. The subsequent Shogen era was changed again two years later, presumably due to continued famine and epidemics. A team of archeologists cite the Azuma Kagami and state it "describes the Kamakura of those days in which natural disasters, famines, and an epidemics occurred frequently, and where dead bodies of humans, cows, and horses, etc., filled the roads." Furthermore, they provide archeological evidence to support their finding.

In 2013 geoscientists, triangulated by chemical tests and anthropological evidence, were able to find conclusive evidence that in 1257 there was a hugh volcanic eruption in Samalas Indonesia which injected aerosols into the atmosphere of such magnitude that it reduced the solar radiation reaching the Earth's surface, cooled the atmosphere for several years, led to famines and crop failures around the world, and perhaps helped trigger the "Little Ice Age." This may have precipitated the Shoga famines of 1258 and 1259 (See 1 and 2).

I hope these sources cast some light on the matter.