I had to do the same thing when we bought a new refrigerator. I used the
flush trim method and that worked except I couldn't get to the ends because
the router didn't have enough room. So I finished up on each end with one
of those Japanese pull saws very carefully. It looked very nice and the
only thing I had to finish was the bottom of the cut. Then it wasn't
noticeable.

After I pushed in the new refrigetor no one could see my pains taking work
because the refrigerator sticks out 10" farther than the cabinet. I am 6-3
and I am the only one in our house that can see it when I stand up on my
toes.