Fluttering through the night skies over Kagoshima prefecture, this innocuous-looking specter at first appears to be nothing more than a strip of white cloth about ten meters long, until it drops onto its unsuspecting human victim and wraps itself tightly around the head and neck, attempting to induce death by suffocation.

Although in appearance the ittan-momen seems like some sort of tsukumo-gami, a man who once fended off this cloth bogey's attack with his sword was left with blood on his hands when the apparition disappeared, perhaps indicating that this monster is a shapeshifting animal's transformation.

Aside from this story, are there other stories that could support the theory that an ittan-momen is really a shapeshifting animal's transformation and not a tsukumo-gami?

Well, with that particular story, I guess that blood doesn't necessarily mean that it's not a tsukumogami (although we might assume it's not). But also, tanuki sometimes transform into objects, so in theory a mujina or tanuki could also take the form of ittanmomen as well. Also, that particular story of the man was from the end of the Heian period, if I remember correctly - in the Konjaku Monogatari-shuu, but that story is based in Kyoto (formerly Heian) itself, as opposed to Kagoshima (which is where this youkai is generally considered be to "from"). Obviously not saying that it can't go to other parts of the country, especially when it can fly, but Kagoshima and Kyoto are pretty far apart (both being on different islands as well), considering how difficult it was to travel during the Heian Period, so it seems strange that it might be the same type of youkai. Again, like I said, it could be something else taking that shape - and as tanuki and mujina sometimes take the form of supposed "inanimate" objects...
However, to answer your questions, as far as I'm aware and have found, the only version where the ittanmomen(-like youkai?) bleeds is from the Konjaku.

But like with most youkai, I doubt there's a simple answer. From what I read, there's a similar being in China - called (in Japanese) Kushuu-sankai (a group of 3 creatures - an ogre, a cloth, and a duck). It features in a story written in the 1770's, so there's also the chance that the author had heard of the Japanese version and wrote it into the story, or that kushuu-sankai actually a Chinese creature. Unfortunately, I can't find much about it in Japanese other than a basic description (and Chinese is beyond me).

heh, this particular creature is featured in a DS game called Izuna 2. It's one of the more annoying creatures to take down ><.