Thanks Majestic. I seem to have hit a dead end on these characters. Time to focus more on the blade than the signature. I am still skeptical of the antiquity of this blade. The rust patina on the tang does suggest age but what little I can see of the hamon looks fairly regular rather than wavy. Unfortunately many have handled this blade over the decades without regard to the damage fingerprints can do. I will try to get someone at the Boston Museum of Fine Arts to have a look at it. They have an extensive collection of Japanese swords and I am hopeful that one of the curators can accurately evaluate its quality. If it is a good blade, I will consider finding a competent person to polish it.
My father fought in the Pacific from very near the beginning all the way to the end. No matter what its quality, this sword is a meaningful addition to my artifacts from that time.
I just noticed that K.Morita on the other board pressed the "like" button for Matt's post where Matt guessed "守次" (Moritsugu). Morita-san is the resident expert on grass script on that board. When he gives an upvote to someone, it usually means he agrees with them. So I would look at Moritsugu 守次 as a very strong possibility. Think about a date sometime in the 1800s for the sword.
Our native-speaker here on this board (@Toritoribe) may also have an opinion on that reading.
For me, the more I looked at it, the more I convinced myself that the second character was 貞 (sada). And the more I looked at the first signature, the more I convinced myself that it wasn't 守. So I was leaning towards a signature of ＿貞, of which there are many.
Anyway, your strategy of looking beyond the signature to the sword itself is a good one. A great sword with an illegible signature is much, much more valuable than an average sword with a legible signature. In this respect, the sword world is slightly different from the world of paintings and other collectibles. It has its own dogmas and idiosyncracies, but it does tend to focus on the quality of the sword first, and the quality of the signature second.
Hah, I missed the endorsement of K. Morita. Thanks for pointing that out.
MFA no longer has a resident expert as Mr Ogawa has returned to Japan. However, next week is my lucky week. The auction house Bonham's is holding an auction of Samurai artifacts including swords here in Boston on the 27th and one of their in-house experts from the New York office may be present. This may be a chance to have a knowledgeable person see the blade close up.
I initially thought the second one was 次, but indeed the circle at the middle of it is closer to 貞. However, the dot at the upper left is odd and a vertical line is necessary above the long vertical line for 貞. Hmm...
@Toritoribe, as I understand your post, you do not favor either character that has been suggested for Moritsugu 守次 . There is some convergence on the second character which could be 次 or 貞 . It seems to me that the first character is crucial to making further progress. This investigation has taken some interesting twists and turns. From my perspective, I am fascinated by the stylized characters and wonder if the swordsmith was as creative at the forge as he was with his signature.
I have included this photo to show the oxidized patina of the tang which speaks to its age. You may see something in the original that my photoshop enhancement has not captured.