Electrical – hole in drywall too big for old-construction electrical box – what to do

I would clean out the area around the holes to give myself room to work without being showered with cellulose. Open the holes a little: make them square, and big enough to be able to get your hands through. Next, get myself a roll of R-13 fiberglass batting (currently less than $10 at Lowe's or HD), and cut patches to fill the void in the cellulose insulation: you'd probably need two or three layers, depending on what size your ceiling joists are. Stuff them through the holes and spread them out. Finally, use a couple of 1x2's to cross each of the holes, and patch them as described in this answer to this question.

I've used a shop-vac for cleaning up blown cellulose, but for disposal, not for later re-installation. It seems to me that it has a very different texture before and after: clumpy and with some structure, versus powdery, no texture.

It is hard to tell from the picture but I am guessing you are using a traditional screen and you are moving the screen back and forth along one of the axes of the screen. If the less than stellar ascii art below is your screen, instead of instead of moving N-S or E-W move the screen NE-SW or NW-SE. Or start with the screen rotated 45 degrees and continue to sand N-S or E-W

+--+--+--+--+--+--+--+
|  |  |  |  |  |  |  |
+--+--+--+--+--+--+--+          N
|  |  |  |  |  |  |  |        W + E
+--+--+--+--+--+--+--+          S
|  |  |  |  |  |  |  |
+--+--+--+--+--+--+--+

A lot of times primer and paint will fill in these tiny scratches and most people will not notice even if the scratches are not filled in completely. But since it is your house and the scratches bother you go ahead and try the diagonal movements.