From what I can find, you will have to deal with an agency who will take care of the details. I was not able to find a way to deal directly with the sword smiths (which is understandable considering their work.)
That being said:
The Seki Sword Tradition Museum has, as you said, occasional demonstrations during the year. There is one on January 2nd, and one during the Seki Cutlery Festival. You should confirm this as I could not find conclusive evidence, but for 2016, it seems as it will be between October 8th and 10th.
They also offer demonstrations at other periods of the year as can be seen here.
Toki offers demonstrations with master sword smith Yoshindo Yoshihara. I suspect it might be expensive, but this is likely to be the closest to what you want to see as you will be visiting the master directly in small groups.
Govoyaging offers a visit that allows you to forge your own knife under the supervision of master sword smith Asano Taro.
Note: This is unavailable for September and October, but if you can extend your trip slightly into November, you will be able to go.
The Bizen Osafune Museum offers demonstrations and courses around the year. The schedule for October has yet to be updated as of July 11th, you will have to check back later.
Inside Japan Tours offers a 3 hour tour of a sword smith's workshop in Nikko.
(Note: I have never dealt with this company, but it seems that you have to reserve your entire trip with them to benefit from the visits.)