Remove the old stove top and do some layout work on the counter. I've marked the center lines of the old stove top on the green tape. The hash marks are "no cut" zones. There's some cabinet structure under there that we don't want to cut into.

Make a pattern from the new stovetop by tracing around it, then making a second line inside the first one 3/8". The inside line will be your cut line. Line up the center lines of the pattern with your old stove top center lines and check things out.

You can see we'll have to move the new stove top to avoid the "no cut" zones. Also check under the cabinet top for wire harnesses and plumbing that may need to be moved. I ended up moving the pattern to the right and back 1". I also moved a wiring harness between the sink and stove over a bit but it was just a matter of relocating a few clamps. You can see the edge of an electrical outlet poking into the bottom of the photo. The old stove barely cleared that outlet, and I'll end up moving the stove back. There's plenty of clearance. 

Here's how the saw line ends up. No more interference with the "no cut" zone. We don't quite have enough existing counter top in the lower left corner but the mounting flange of the new stove top will cover that.

Here's that little bit of the old stove top cutout but it's not going to be a problem.

Reattach all wiring harnesses, drop in the new stove top and secure with three screws. Drop the old stove body into the new stove top and secure with 4 screws, reattach the gas and put the old stove top back on, securing with 2 screws. Done.

Here's the old stove cover sitting on top of the new stove. You can see it's about the same size as the new stove but sat 1 1/2" above the counter.