The day had to come, I guess, when I wanted to do something for which applique, rather than piecing, seemed like the best way forward, and that day is today. I've gone all around the houses thinking it over, but no other answer seems right. So applique it is.
This means that right now I am not machining at all, which in turn means that my production has gone from slow to slooooooow.
This is what it looks like right now.
I'm hoping I'll get the hang of the applique okay (and please don't look too closely at my stitches, or tell me it will take years to get it right; I need it to work now, or at least now-ish) but any helpful tips more than welcome!