The Jaeger-LeCoultre Master Grand Reveil is a real marvel by any standard. It wear dressy as easily as it does sports chich. But yes you need to strap it on tight. I once saw it on the same brown strap that the IWC Big pilot has, in brown, It looked very cool too. Well soo cool that I asked the gentleman if he would sell me his strap and the nice man was very accomodating as for him it was his old strap for me it was a nicely broken in one. Nice gesture from him. In any case I never tried the starp but at least I know I have it when I want to swap.
Back to the JLC I keep this puppy on a winder being a perpetual calendar and it seems to be happy.
Good luck on the hunt.
Bill