Are you sure about the 58" distance? It sounds more like the distance required when there is no hood over the rangetop. If a hood were mounted that high, it would be pretty ineffective, since the effluent would have so much opportunity to escape before the hood could capture it. When there is a hood over the rangetop, the distance between the cooktop and the bottom of the hood should be between 30-36".

Having said that, I am not a fan of a wood-enclosed hood when there is a griddle beneath. Griddle cooking generates a lot of smoke and grease that will collect on the wood enclosure, which will then be hard to clean off.

If you go ahead with the wood hood enclosure, make sure the depth front-to-back is at least 24". The wood hood enclosures are notorious for being made too shallow, like 19". You need to make sure about that.

Is your contractor paying your next 20 years of fire insurance? If there is a fire, not necessarily due to the combustibles height, the insurance company may not pay on the ground that the installation violated requirements. The Code Enforcement officer should also catch deviations like this.

Please check any diagrams that the installation guide provides for the bounds over which the 58-inch rule applies. Perhaps if the front of the cabinet is actually beyond the extent of the range it will be OK from a hazard point of view.

In some cases, such as the wall requirements when back-guards (risers) aren't used, the issue is not immediate fire, but wood deterioration making fire easier in the future.

I agree with @Shannon_WI that 58" sounds off.

We've had wood surround hoods over our Wolf griddles for 18 or so years and now over our BS RNB griddle. No problems w/ grease buildup.

FWIW, Elica hoods have zero containment volume and are not known for being quiet. I'd look at a different insert along w/ a remote blower and silencer.

More: https://bamasotan.us/range-exhaust-hood-faq/