Andy, I have fitted MC exhaust pipes on my GT 4.2, which puts me in your solution #2 camp ie. sport mode 24/7
It is definitely bearable. I was afraid abt the noise level in the LT so I had bought the valve kit from Formula Dynamics over in the US. After 6months on full on exhaust, that valve kit is still in its box, sitting in my basement.
Another interesting perspective... I live in central London in a terraced house, w plenty of neighbors, and the car sleep in the street. Despite starting it every morning around 7am, none of my neighbors have sniped me or slashed my tyres yet.
So if I can handle it as a DD, and my neighbors can, I think you should be OK.
My only concern would be resale value. People will def expect the on/off noise option.
If nobody can fix your exhaust (which other members infer should be possible), you can always sell the "always on" old back boxes, and buy new ones from OEM. The net differential cost might not be too bad, as I really think you should get at £1000 for the old ones.
