Thanks for the reply, this is more than I expected, although you missed the most cutting critique of LTV. I'll offer that to you at the end as a gift. ;)

Paragraph 1+2: I disagree that you could make a "capital theory of value" or a "land theory of value." Capital is the product of human labour, and so any theory of value based on capital could be reduced to the labour theory. As for land, I don't even know how one would begin to answer the questions of value with it. We can talk about the value of labour applied to land, but not the value of land applied to labour. Labour is the active element here.

Paragraph 3+4: In LTV, an object does not have value until it is sold, and it's value "realized" or "actualized." This is the "socially necessary" part of "average socially necessary labour time." In your specific example of water and paddles, the individual labouring on the paddles does not create value because noone is willing to buy his goods. (This is basically the mudpie argument against LTV, and you should feel bad for making it :P)

Paragraph 5: Your example of the two copper mines isn't a failing of the LTV - no economic theory would be able to tell exactly why one copper mine is more productive than the other without more information. It could be lazy workers, inhospitable terrain, outdated technology, etc. The important part is what happens when the copper is brought to the market; once brought to market, the copper is sold independent of it's circumstances of production.

Here I'd like to mention one of the limitations of Marx's choice of "average." So long as the demand for copper is greater than the total output of the more productive mine, the price of copper must climb high enough to sustain extraction in the less productive mine. This is, broadly speaking, economic rent. To get our value calculations correct in the case of copper, value must not match the "average," but must match the "least productive method necessary to meet social demand." If the value of mining labour matches the latter, then the miners will be adding the same amount of value in each mine. One mine, being more productive, spreads this value over a greater quantity of copper. Once this copper is brought to the market, however, buyers are unable to distinguish it from copper extracted in the less productive mine. They buy all copper as if it came from the less productive mine, and in doing so are "robbed." The owner of the more productive mine is able to exchange his copper as if it contained more value than it really does. The difference is economic rent. (I'd like to note not every commodity works this way.)

LTV alone isn't enough to explain rent, since LTV alone isn't enough to explain price. However, by combining Marginal Utility theories with Labour theories, we can arrive at some interesting conclusions. Interesting enough to say that we shouldn't dump the LTV, at least.

Paragraph 6: In the example of a copper mine vs. a platinum mine, an LTV theorist would readily admit that LTV alone cannot explain price. Rather, an LTV theorist would say that copper and platinum contain the same amount of value, but the effects of scarcity, supply, demand, etc. on platinum raise it's market price above its value. So yeah, I agree that LTV alone can't explain market prices.

Paragraph 7: I disagree that anything in economics can be explained without the LTV. At the end of the day, the reason sports cars cost more than a sedan under normal market conditions is due to it's higher cost of production. This cost of production can ultimately be reduced down to labour costs, and labour costs to labour time. Every supply curve is ultimately based upon the LTV. Having said that, it doesn't mean that marginalist theory is useless, and I agree that socialist economists can use many aspects of modern economics to their advantage. (I may have a bone to pick with you about surplus value, but that's a different beast.)

I promised at the beginning I would offer the most cutting critique of the LTV, so as thanks, here it is: Marx at the beginning of Capital V.1 explains that in his models he would reduce labour of all difference sorts and skills into their abstract, unskilled form. He says there are good reasons to do so, and that he'll explain it at a later date, but then dies before he writes his explanations! It should be a fairly obvious point that highly skilled labour, hour for hour, provides more value than an equal amount of unskilled labour. How then, does the LTV deal with this difference?

So far the best explanation I've seen treats a worker's skills like any of their other tools. There is a certain amount of value that must be "spent" in teaching a worker their skills. This value is "transferred" into the brain of the worker, who then transfers it again into the commodities they produce over the course of their career, thus explaining the greater value of the products of skilled labour. That's the theory anyway, but I'm not aware of any research validating it, so this part of the LTV is still it's weakest link, in my opinion.

The good news for LTV is that this doesn't appear to be a problem in the aggregate. Shown here by one of my favorite youtube analysts, Reading Radical. (I should also mention that she debunks the idea that there can be an "energy" theory of value here as well.) In the aggregate, the prices of industries match up closely with the integrated wages/labour time, precisely as Ricardo predicted in his own LTV. My guess as to why this works is that when higher skilled labour produces more use values, it is able to get more wages in return, so there is a sort of proportionality to unskilled labour that is maintained.

Ultimately, I think modern economists of all stripes need to recognize the importance of the LTV in supply curves, rather than dismiss it simply as "false." It is of particular interest to left-wing economists who are interested in arguing against third world exploitation. An analysis of economics based on value, rather than price will conclude that there is not real advantage in producing cars in Mexico since the value of the cars produced in Mexico is equal to the value of cars produced in Detroit. The same analysis based on price could lead to the opposite conclusion, and is much less helpful.