It is a bit hard to see, but it DOES look as though the hamon goes straight back into the nakago rather than tapering off. I did not touch the rust and crud on ANY part of the nakago, even where the habaki covers it, as I have always been told to NEVER touch the nakago, no matter what (the rust can help determine the age of the blade, or something like that). So my scrubbing stopped at the machi. The blade itself is 14.7" from the hamachi to the tip of the kissaki.
As for the sword being Edo, that is what Daimyou on Evilbay was selling it as. I have heard that he is honest, though the blades he sells are either very tired or in bad need of restoration (like mine).
Are nagamaki naoshi fairly common?
The sword came with a battered but intact saya that has a badly worn koiguchi and a kozuka pocket, a rather battered copper habaki, and an old tsuka that not only was apparently of poor quality (the remaining samegawa was not wrapped, and not even in inlaid panels, but pieced together and glued on), but didn't even go with this blade (the mekugi ana in the tsuka did not even come close to lining up with the one in the nakago).
I don't know if the saya is worth saving and restoring or not, or if it can be taken apart and the inside cleaned, the koiguchi shimmed to fit the habaki, and the outside relacquered, or if I should have a totally new saya made for it along with a new tsuka. First priority, or course, is to have it polished and put in shirasaya. While I am not good at outside contouring of wood, I am good enough at wood working to inlet the blade into a crude-looking but protective shirasaya that will keep the blade safe after polish, until I can afford to have a professional make proper koshirae.