From an academic viewpoint, the emphasis would be on locating the 'earliest' verifiable biography of Higaonna Kanryo - working on the premise that the details contained within it are probably correct. This would lie with the Miyagi family today - but with other general (Okinawan) historical evidence supporting certain key facts. From what I have seen so far, all the Chinese language records seem to be gathered from either Okinawans bringing the data to China - or Chinese explorers and/or scholars visiting Okinawa and seeing the evidence with their own eyes. As Ryu Ryu Ko and Go Gen Ki are both recorded as being ethnic Chinese people, the fact that even in China their names are recorded in an early Japanese phonetical script - would support this view. If these records were made in China, then the names would have been carefully recorded in traditional Chinese script and we would know exactly who they were and where they (and their families) came from.
The next logical question would then be 'when' were these records acquired? We know that it must have been after Higaonna Kanryo left China and returned to Okinawa - as it was himself who brought all this data to Okinawa. This would be the post-1879 era following Japan's annexation of Ryukyu and the loss of its 'Chinese' status. Time must be allowed for Higaonna Kanryo to settle back home and for his acquired 'Chinese' knowledge to be more broadly known. After-all, if he had remained silent and taught no one - then we would not be having this conversation! Perhaps if we allow ten years for this process - this takes us to the post-1889 era. I think this is a good assumption for an 'earliest' starting date of Higaonna Kanryo's journey to China becoming 'history' in a conventional sense.
What would be the cut-off date? Well, we know that this was the Battle of Okinawa which was fought between 1.4.1945-22.6.1945. Repeated historical records state that all (or most) of the physical (historical) evidence of Higaoona Kanryo's life (and that of Miyagi Chojun and other Goju Ryu practitioners) was destroyed during this devastating encounter! To be clear, this is the historical artefacts such as documents, texts, lineages, histories, manuals, certificates, drawings, photographs and travel documents, etc, alongside objects such as training clothing, training devices and weaponry - were all lost in the conflagration! This applies to all the historical evidence gathered by Higaonna Kanryo, Miyagi Chojun and Wu Xiangui!
Therefore, logic gives us a time-span of between 1889-1945 for the historical evidence stored in Okinawa (relating to Higaonna Kanryo training in Fuzhou) to have been carried by Okinawans to China (where it was written down), or gathered by Chinese visitors to Okinawa (where it was written down and conveyed back to China). Of course, both modes of transmission may have happened (in unconnected ways) as we have no way of telling. This can be further refined by stating that with the outbreak of the Second Sino-Japanese War (1937-1945) - it is unlikely that ethnic Chinese were allowed to travel to the Japanese occupied island of Okinawa. On the other hand, those considered ethnic Japanese (such as the Okinawans) - were encouraged to actively migrate and traverse through the ever expanding Japanese empire - with large swathes of China falling into this description! (This observation does not apply to Taiwan - which had been a colony of Japan since 1895. By the time of WWII - these Chinese people were thoroughly acculturated into thinking they their 'Japanese' - even forming Regiments in the Japanese Army and fighting the 'Chinese' in Mainland China).
The ethnic Chinese collection of data from Okinawa would then seem to fit into the time-span of 1889-1937 (48 years) - whilst Okinawans travelling to and from China probably stayed possible right up to the end of the Pacific War (1941-1945) and Japan's eventual defeat at the hands of the Red Army (the Soviet-Japanese War fought August 9th–September 3rd - 1945). The Okinawans, then, could have travelled to and from China between 1889-1945 (some 56 years). From 1945 onwards, according to the history books, all tangible evidence for Higaonna Kanryo's visit to Fuzhou (and training in training in Fujian White Crane Fist) 'disappears' - but according to witnesses - did once exist! What I would be interested in, (and will endeavour to locate), is the 'earliest' Higaonna Kanryo biography extant within Chinese language sources.