What's the proper procedure for replacing ungrounded circuits?
I seem to recall (not from a handy chunk of code, just from talking with an electrician I work with sometimes) that abandoning wire is generally a no-no (not sure if that applies when  it's inaccessible and impractical to remove, which might make the exception.)

Fishing wires up or down exterior walls that have insulation in them will be potentially frustrating, to say the least.

334.30(B)(1) would appear to allow this, and 334.30(B)(2) only says it applies in accessible ceiling spaces. 334.30(B)(1) (an inaccessible, impractical to support space in an existing finished structure that wire is fished through) appears to apply, without a specific length limit. But they don't get a lot of points for clarity.

If you are opening up to put in larger boxes, you may be able to staple the ends of the cables before you set the box (reaching through the box hole.) Doing so won't really buy much though, since that end will be supported at the box. You definitely want to fish the wire before you set the new box.