I’m curious what the convincing circumstances were. Especially given the “mild-mannered” nature with which you wish to drive, I don’t see much of a point in spending the money. That said, a limited-slip differential presents none of the issues you mention. I installed an MFactory helical LSD, and it is without a single issue—no clunks, no noise... just a grippy 10% torque increase (3.38 versus 3.07) at the wheels in all gears that, also, significantly reduced the intrusiveness of the traction control. Any car with limited slip is better than a car without, but the question is whether the improvement is leveraged and worth the money.
2004 BMW 330i ZHP (52k miles), Jet Black with black leather, MFactory LSD (3.38) with Z4 cover, 18"x8.5" ET38 APEX Arc-8's (Anthracite) with 245/40 Michelin PSS', Koni Sports with factory springs and front and rear reinforcement plates, Shark Injector, Corsa TSE3 cat-back exhaust, TMS under-driven pulleys (water & steering), CDV delete, TMS CF strut brace, K&N CAI, GAS DISA rebuild, TMS pedals, Wheelskins steering wheel cover, roller tray center console, black-out grilles, and WeatherTech mats