I did this recently & had planned to use the router ... did, in fact,
except in the places you described where it wasn't manageable (would
have been possible with a jig, maybe, and/or a longer bit designed for
such things). I ended up finishing with a sabre saw (same deal with the
sink cutout). The formica chipped in one spot, I think because I was
pushing the saw rather than letting it cut.

Anyhow, I got a nice clean edge that didn't need much fixing before
gluing the end cap on. Most of my sabre-sawing was on the back, but
when I did it on the front I protected the countertop with masking
tape.

You can put tape on the saw instead, but in my experience it wears
through more quickly.

I'm no expert, having replaced only one countertop in my life. It came
out okay. If I had paid a professional, I would have expected (and
certainly gotten) better results ... but I wouldn't have had as much
fun OR been able to convince my wife I needed more tools.