Re-reading various books on Japanese cloisonne, the historical sequence seems to be:

1838 Kaji Tsunekichi reverse engineers cloisonne from a Ming piece
1850 Daimyo of Owari becomes patron for Kaji Tsunekichi
1853-56 Kaji takes on two pupils, Yoshimura Taiji and Hayashi Shogoro
1858-59 Perry expedition forces opening of port of Yokohama for foreign trade
1860-63 Go-getter Hayashi Shogoro takes on a student, opens a cloisonne factory, walks from Nagoya to Yokohama to smuggle his cloisonne to sell to foreigners (export of copper was forbidden)

1865-1874 "Middle Period" cloisonne sold abroad. Somber enamels, tiny fabric-derived patterns [with a distinctive little cloud pattern featuring a circular center], dull matte surface with much pitting - referred to in Japanese as Doro Shippo.

1870s - new enamel technology ends use of Doro Shippo enamels.

Some pics of an ojime that, judging from the enamel and motifs, seems to fall into the 1840-1870 timeline for Doro Shippo. It's a somewhat flattened sphere - the pictures are accurate.