I've suffered quite a few of these terrible "hot starts" incidents in my time and thank God, I've survived them all.
During some of them I turned off the booster pump which brought the T4 back within limits. During others, on a different type of helicopter, I switched off the engine, as per the manufacturer's advice, before the T5 limit was exceeded.
Good old Air Traffic Control always helped by saying useful things like "A bit more left rudder, Captain!" and "Hold her steady, Jim!" I said "Thanks, but my name's not Jim!"
Fortunately, the aircraft didn't ever try to send me into oblivion, they just sort of.. er, sat there on the ground.
Strangely, one thing I've never been able to explain: It didn't matter what type of turbine helicopter it was, they all made a noise like a piston engined Bell 47.
P.S. Does that make you want me as the hero of your new book, or just the technical adviser? I usually charge by the hour but I'm pretty cheap. Or, by arrangement, a one off payment in advance will be OK.