Here's the progress in the next 24 hours —mostly due to an insomniac hour Sunday night, after I took the previous pic. A few familiar faces are starting to emerge.
I'm following a modified version of the program Yellow Oval has spelled out—alternating between faces and edge pieces. The colors and distinct lettering style of superimposed "sound effects" are also pretty helpful for grouping pieces that belong next to each other. I'm boxed in by my small table and feeling the need to rearrange some of these sub-assemblies, so I may bust out a spatula for the next session.
That may not be until the weekend, since I have work deadlines every day the rest of the week, but if I get in a session before then I'll post the results.
BTW, we have a cat as well. At the suggestion of a friend, I cover the pieces with a tablecloth bewteen working sessions. It cuts down the "add a few pieces in passing" factor, but keeps the pieces out of the wrong paws.