The full theory of prices is only explained by Marx in the context of competing capitals, and the full development of M-C-M', but Marx does clearly accord correspondance between values and prices, even if they're not the same thing, and they're at different levels of abstraction. Marx does offer an argument for why labour is taken as the substance of value (and why socially necessary labour time is its magnitude) - and it's all developed further in the analysis of money. Yes, "labour" doesn't correlate with price in Marx's schema, but the "amount" of abstract labour, determined by the socially necessary labour time required to reproduce a commodity, does.
Shaikh and Tonak show that in the case of freely reproducible commodities, excluding things such as natural resources and land (covered in the theory of rent instead), some empirical research does show correspondance between labour-values and prices in subsets of the economy where it can be measured.
Marx's theory of exploitation requires a correspondance between wages (as money) and value (the product of the labour process). It wasn't as though Marx saw an inconsistency and ran with the theory anyway. Unfortunately for his detractors, the same arguments since Bohm-Bawerk have been repeated since they were made despite adequate refutation by those who hold to Marx's "LTV".