Feels to me like Ishitoya (said with a bit more confidence, thanks to your magnified images). And I would say its the photography studio name, rather than the subject's name. There are multiple pronounciations; Ishitoya, Ishidoya, Sekitoya, Sekidoya. The pronunciation doesn't matter too much yet, as long as you have the kanji.
As to next steps, this really is a tough one. If you knew the name of the family, or even the name of the town they were from, I might have some optimism that someone could be found who could identify the relatives. Right now, the photos and the possible name of the photo studio are the only things we have. The partial name on the sword won't help identify the family. There are groups (including the Japanese embassy) that help repatriate war items, but somehow I feel there isn't enough info for these groups to make a connection. As slim as the chances are, I feel it might be best to just continue posting to forums like this, or maybe try one of the militaria-related forums to see if any info can be gleaned from the uniform in the picture. Its a very handsome family, and the fact they got the whole family photographed makes me think they have some money. Ishitoya is not very common, but it isn't ultra-rare either. People with this surname tend to come from the north of Japan; Aomori, Akita,
Hokkaidō.
The sword, while very symbolic and a nice antique, presents a kind of dilemma for the family, even if you do manage to find them. If it were a sword of high quality and rarity, the family may gladly accept its return, and go through the hassle of re-importing this item. Swords need to be registered upon importation, and this can be a burden. Many families aren't aware of the regulations, and many are under the mistaken impression that you need to have a special license to own a sword. But a cut-off sword missing half the name, makes me think the sword is not so precious. This is just wild speculation...I could tell more with better pictures of the blade and the tip itself. The sword furnishings are not so interesting - its the blade itself which is important. This is the long-winded way of saying you have a Sisyphean task ahead of you trying to repatriate these items, as there is a chance the family may not be interested in receiving it.
So start with the photos and plaster them where you can; war-related forums, genealogy forums, maybe Facebook and Reddit and Twitter. Then see if you can get any leads from there.