I could see spending hours on the internet trying to find a switch that both fits and is more sensitive, only to buy something that in the end doesn’t fit. Random parts defeat. But if you find something that would be really helpful to everyone!
How much free play do you have? You could just adjust that bolt so that the lever’s resting position is closer to actuated. Would that help?
But MOST OF ALL put a cotter pin in that hole ASAP! Mine has one.