Here are some good sources but a poor answer.

You might be interested in a book by Dan Linger, No One Home. It looks at Japanese-Brazilians who were allowed back into Japan under favorable immigration policies. While it doesn't answer the beginning of your question, it answers the "end" and will balance out sources that look at the initial stages. Identity often gets defined in opposition. Japanese-Brazilians may feel Japanese in Brazil and Brazilian in Japan. Sources focusing on immigrant experiences within Brazil might exaggerate differences to construct their own identities.

A cultural founder effect should also be kept in mind. I have not read it but Albion's Seed by David Fischer examines how the origin of migrants from different cultural centers in England affected American Culture. Japan, like England, has a number of distinct cultural centers such as Okinawa or Kansai. Okinawans are about 10% of Brazil's Nikkei population. According to New Worlds, New Lives, Okinawan politicians often rely on a "Japanese" identity when appealing to the rest of Brazil. They themselves may feel conflicted with "Okinawan" and "Japanese" being seen as distinct. These regional differences which are not perceived outside a group may play a role in the degree of "assimilation." Though, Okinawans may be a slightly complex case for historical as well as linguistic reasons. Even if you more narrowly focus on Honshu, Tohoku, Kanto, and Kansai have distinct enough cultures that thinking about "Japanese" might obscure differences which could matter as much as would referring to Italians rather than Venetians and Sicilians.

New Worlds, New Lives looks at Japanese migrants to seven countries: Argentina, Bolivia, Brazil, Canada, Paraguay, Peru, and the United States. It should help fill out the role the new home culture can play in shaping a sense of identity.