For me, it is not possible to have "a set of all sets" (include itself), but it is possible to have "a set of all other sets" (other than itself). It is necessary to restrict conceptualization only in term of non-self-contradictory. Because, is it meaningful to make a concept such as "even odd-numbers"?
Since, there's no possible for self-contradictory concepts to exist, then, it shouldn't be conceptualize in the first place. And, in my opinion, "a set of all sets" (include itself) is one of self-contradictory concept, which shouldn't be conceptualize in the first place, rather than presuppose its existence and try to figure out the consequences of it.
About what Russell says, "The class of teaspoons, for example, is not another teaspoon, but the class of things that are not teaspoons, is one of the things that are not teaspoons." My answer is, although "the class of things that are not teaspoons" is also not teaspoons, but it is in different level than "the things that are not teaspoons", in this case we should differentiate between "things" and "class of things".
Further more, Russel says, "There seemed to be instances that are not negative: for example, the class of all classes is a class." Again, here we should differentiate between "The class of things" and "The class of classes". Because it is in different level, so that shouldn't be put in the same class.
And if we could maintain this principle, then the next point that Russel says won't be confusing either. Russel says, "The application of Cantor's argument led me to consider the classes that are not members of themselves; and these, it seemed, must form a class." Now, since we still differentiate the differentiation of different levels, then "The classes that are not members of themselves" is different than "these, it seemed, must form a class", so that the question that arise after that is not necessarily arisen, which is "whether this class is a member of itself or not." Because, the answer is clear: "this class" that contain "the class that are not members of themselves" is contain "the class that are not members of themselves", and not contain itself.