While I was thinking about the implications of the fact that there are other chamber graves in Russia that have similar textile and birchbark box fragments to the Pskov find, I found the following article on line. (It is from a German-titled and thus probably mostly German language publication, though the article itself is in English, so I apologize in advance if the name of the publication and the publisher aren't in the correct format.)
Andrzej Janowski, Early medieval chamber graves on the south coast of the Baltic Sea. Beiträge zur Urund Frühgeschichte Mitteleuropas 60, Der Wandel um 1000, pp. 257-267 (Beier & Beran 2011). [Go here for a PDF of the article; you may need to start an account on academia.edu to get to the page, but the account is free even if you're just a random interested person and not an academic or student.]
The main theme of Mr. Janowski's article is that quite a large number of chamber graves have been found, not just in Russia and along the Baltic Sea coast, but in Scandinavia itself. He reports that the academic consensus has been that over the past 100 years the cultural source of this type of grave was deemed to be Russian, but now the source is thought to be Scandinavian.
Mr. Janowski does not discuss any textile finds, and the graves for which he includes sketches of artifacts are male. What he does is discuss a number of finds, made over the past 30 years, in northern Germany and Poland. He states that while the (relatively) newly discovered graves in Poland and Germany bear a strong resemblance to the the Scandinavian chamber graves, in physical structure, most of the artifacts found therein, particularly the female jewelry found in them, are Slavic in style:
All other artifacts discovered in the chamber graves at the Southern Baltic Sea Coast, especially silver female jewelry (temple-rings, ear-rings, “kaptorgi”, i. e. amulet cases suspended on a neck), are typically Slavic. It seems then, that the equipment discovered in the discussed graves, although of luxurious character and proving high social status of the persons or their community, does not prove their foreign origins. Furthermore, while in case of graves from Pień, Kałdus, Sowinki, Dziekanowice or Oldenburg, dated for the 10th – beginning of 11th century Scandinavian attribution of the buried persons would be acceptable, since they come from the period of the highest Scandinavian activity in Eastern and Central Europe (cf. Leciejewicz 1995), graves from Western Pomerania, and Mecklenburg, 100–150 years younger, have no relation to it. (page 265).
So it can't be assumed that an occupant of a chamber grave in, say, Poland for example, was dressed like the Pskov woman, or a Birka woman, unless the jewelry in the grave matches the types found in Pskov and Birka--and even then we can't be sure because the Pskov find was found separately stored and not on a human body. Or it may just be that the Polish and German graves are different for some reason. Clearly, I have to do some more thinking and research on chamber graves, and what appears within them, before I can try to draw defensible conclusions about what they say about women's costume. In the meantime, I commend the article in question to the attention of anyone interested in material culture in early medieval northern Europe.