A brief follow-up on this fax issue, and many thanks to John S for the prompt suggestions.
This was a case of immediate need; rarely the best conditions under which to make a service decision.
Anyway, after surveying several possibilities I selected Fax.to and enrolled for a trial period.
As is par for the course, their promotional material failed to clarify the true costs and limitations. Along with the monthly service fee of ~$22 (after the 4-day trial period), I discovered that there is a per-transmission fee of ~$0.15. Also, it was never made clear to me that I would receive my very own Japanese fax number to use for return faxing. After an initial abortive attempt at usage, I canceled the service.
I again attempted to contact eFax customer service and this time was successful in reaching a human.
After describing my problems with their new and improved user interface (rejects Japanese input), and documenting same with screen captures, the representative assured me that she would pass that information along to their development team.
In the meantime, she gave me a link to use their legacy interface.
So, I am happily back where I started. At least until the next wonderfully improved user interface version comes along.