Studio, not all left-libs believe in the LTV. The founder of the philosophy, Sam Konkin, did not, nor does Roderick Long or Brad Spangler. All of those people are entirely Austrian in economic theory. Even Kevin Carson incorporates subjective aspects in his interpretation of the LTV. However, left-libertarians usually do use a negative definition of capitalism. I know I have. However, no left-libertarian wants to stop "exploitation" through force.
Sam Konkin is the founder of Agorism. By "Left-Libertarian" I'm including the entire "Free market anti-capitalist" tradition, including the early free market anarchists like Tucker and Proudhon. In short, I believe you have a bit of a Frozen Abstraction (treating a sub-class or some sub-classes as if they were the whole
I've heard about Carson and his attempt to synthesize the LTV and STV.
And I agree with you; the left-libertarians don't want to use force. Hell, Proudhon wanted Mutualist-style institutions to compete against (and ultimately compete away) capitalist-style (in the Marxist sense of the term) institutions.
I have respect for the left-libertarians, so I'm not trying to bash you or anything.