Doing it without permission: Worst case you pay for a new car.
Getting permission: Ask!!!.
Find a person who has the authority to approve your request and explain what you are trying to do and why. It actually worked for us.
It's important to find somebody who is able to authorise your request. Dealing with someone who is sympathetic but lacks authority will get you nowhere.
Real life example below.
We rented a car in Australia a few years ago - ALL rental companies had similar "no off road" clauses in their contracts. They were generally specific enough that you could probably drive an Australian "outback" road but not take "unformed road" trails down to picnic areas, dams, lookouts etc.
We had our two adult children with us - we wanted to introduce them to a small glimpse of the "real" outback. We decided to visit and stay at the world famous in Australia "Glengarry Hilton" (yeah, right!!!) - down about 50 km of roads that you wouldn't usually call roads near Lightning Ridge.
Some of the agreements said "without written approval".
The endeavour seemed doomed. Non of the counter staff we spoke to had any expectation that such approval could actually be gained. Nor did their supervisors.
Having identified the company that had the car we most wanted I did an internet hunt for company upper management and found a phone number of a State manager. Instant success. Full understanding of what we wanted to do. Good explanation of WHY they had the policy - and a note that roads to picnic sites etc were fine - all they wanted was a road that had a formal description so the breakdown wagon knew where to find you :-).
He had only one question - "How did you get my number " :-).
Full album here - to stay in roll mode, scroll don't click
Glengarry Hilton - Wikimapia - zoom out until you see where you are :-} . Yes. No problem with driving there. Don't be misled by the "green" surroundings :-).