Hi Alain,
yes, I know the entry about the subject in the copies of the "Meikô zukan" and I think the popular belief is based on the information given in "this book" (or better in the copies and their copies... ). Also Iida san's book relies on this work.
What makes me wonder are two "facts".
1. It is said that the Iwai (岩井), going back to Yozaemon (与左衛門) and Genbei (兵衛), been made mainly two styles of menpô. The Oie-bô and the Etchû-bô. Like mentioned in the MZ.
Well, that means, that they had focused on the one hand of the high quality (and rarely seen) Oie-bô and on the other hand of the Etchû-bô. An menpô in a competely diffrent form, adorned with yasurime (the Hosokawa thing) and executed in diffrent qualities. Thus totally contrary to the fine and feminin Oie-bô, IMHO.
2. The latter ones, or at least the basic shape of this type are seen very often. Therefore it can be assumed, that they were made in large quantitys, probably during the whole Edo period. Admittedly, also without their trademark, the yasurime.
The above in turn forces the comparison with the so called Nara-bô of the Haruta (春田) school. A "mass produced" menpô which could be adepted to the respective customer's request.
Unfortunately, almost all extant specimens are not signed. That makes an accessment considerably more difficult. Furthermore, and that is my main problem, the few signed pieces all refer to Haruta...