I very strongly suspect that I can further qualify the ideal form of the labor theory of value. In my earlier essay, I talked about the "absence of 'complicating factors.'" I think this restriction can be more precisely stated as under conditions of perfect competition without externalities.
Of course, no market is perfectly competitive. One important advantage, I think, of a labor theory of value is that the theory "degrades gracefully"; it still remains approximately true when the conditions of perfect competition are relaxed.
I can think of three ways to empirically confirm a labor theory of value. One is to observe a general positive correlation between nominal price and total raw labor time (i.e. ignoring the "abstract" and "socially necessary" components of the labor theory of value, but including all raw labor time included in capital creation and training/education). Another is to control for other factors, and look for a very close correlation between total raw labor time and price. Yet another is to control for total raw labor time, and look for other factors (subjective labor undesirability, regulation, externalities, etc.) to "pop out" of the data.