Are you saying that the countertop is 1/4" higher than the cook top surface. If the range is taller than the counter top this is not uncommon but is normally adjustable in the legs. More information would help.

Attach as JPEG. NEED photos.

Thanks for the JPEG tip, Fred S. I loaded two photos: a close up and a view of the line of cabinets on the exterior wall. The range is 2" higher than the top of the cabinet. To your point, Lathrem Homebuilders, I'm okay with the range being taller vs. flush with the counter (actually prefer that). The dilemna is once the counter is in with the range sitting taller, we have a 1/4" gap.

So, the non-standard thing here is that the counter top is only 1.25" thick instead of 1.5"+ thick. The lip of the cook top should rest on the counter (arrow in picture #1). Cutting down the doors will ruin the lines (picture #2). What color will your top be? If it is easy to get a paint color match, the proper thing to do would be to put a filler of 1/4"+ on top of the cabinet before the counter top goes on. IMO, with a 1.5" overhang, you would never notice it except that you would already know it is there. I think you will notice the uneven doors way more. If you can't match the counter top color, then match the cabinet color and put a bead detail on the top of the cabinet with the filler.

The countertop is San Gabriel black honed. The cabinet color is Alpine White from Brookhaven, but my non-cab moulding (crown, baseboards) are DM White Dove. A near match. I think you may be on to something. If I understand you right, possibly lay plywood on the cabinets in the 1/4" height with the counters on top. Then around the outer edge either paint the straight edge or possibly add a 1/4" moulding under the cab to hide the plywood build up. Does this seem reasonable? The door style is edgemont, so a bit more detailing than a shaker. Could work out well. Hmmmm...

1/4" tempered hardboard or 5/16" if you can find it. It can be shaped and smoothed to paint the edge. No molding required.
http://www.menards.com/main/building-materials/panel-products/industrial-panels/hardboard-pegboard/1-4-4-x-8-tempered-hardboard/p-1986923-c-13340.htm

I think this may be "the" solution. I'll confirm. In the meantime, thank you, Fred S!

I understand now.

Have you already ordered the slab material? It appears that the cabinets were designed for 2cm material with a laminated edge and a sub-top. Who designed the cabinets and specified the countertop material?

If you are stuck with 3cm material then depending on your edge detail you could use a mitered edge on the front of the slab to hide the sub-top that you need to install to lift up the countertop.