Hi Ed. First off, the range top manufacturer should have included the cut-out dimensions with the unit. Lacking those instructions, I would flip the top over and proceed to build a template that will fit around the underside of the unit. After having made the template, you have two choices. 1) double stick the template to the counter top and use a trim router to cut the hole. 2) Use the template to draw an outline of the hole. Then drill a hole at each corner and use your jig saw to cut the straight-line sides from hole to hole.
When I install an Elway stainless sink last winter, I spent a lot of time making a template for the sink underside. One of my considerations, like you, was the spacing to the back splash. I cut the width of the back edge of the template such that when it was pushed up to the back splash, the cutout was positioned properly. I used option 2 above.
The cutout doesn't need to be pretty, but it definitely needs to be the correct size.