A u-turn would be an easier option...
Although expedite climb is not recommended, if you desperately want to get height quickly it's likely the best option as it'll trade all your excess energy for altitude.
I think you might be misjudging the severity of the notam though, which is really for discouraging routine flight within missile range. After all, if you had a depressurisation or engine failure you're going to end up down there anyway.