Sounds like you are doing enough work to the kitchen that it would actually be more cost effective to order all new cabinets designed for the configuration that you desire than to try to modify what's there. The labor to do all of that will be prohibitive, and you won't even end up with what you really want. As in yes, the contractor is correct. There is no good way to fit a 36" cooktop in a 30" cabinet without compromising it;s structural integrity and the support of the countertop above.

This should not be a problem for any competent carpenter.

Against my better judgment, I will succumb too internet dentistry in extracting the full and complete, existing, conditions.

Thus far the discussion has been directed at the base cabinets.
How about the uppers?
How is the present appliance being vented?
Is your new cooking appliance going to be a "HOB" or a commercial unit that may require a 42" venting appliance?

It can be done.
It all depends on your buget.
snoonyb raises some good points.
What's the design of the cabinets next to the 30"?
Upper drawer modification might be needed.
Only you can decide the route to take.