Not really, since you are swapping an easily available commodity ‘mud’ for bread and fillings. You should specify that the value added to the mud would be unequal to the value added to the sandwich ingredients to make the point you want to. Since you begin with different initial conditions you ‘muddy’ the conclusions.
OK, here's another refutation of the labor theory of value. A woodworking crafter with twenty years of experience takes five hours to make a bookshelf. A person who just started woodworking today takes twenty hours to make the same bookshelf, but it is out of square, out of plumb, is wobbly and has several nail holes in it. According to the labor theory of value, the noob bookshelf is worth more because the laborer took twenty hours to make said shelf, instead of the five hours of the efficient crafter.
OK here's my third refutation of the labor theory of value: you and I both have 1,000 hours of experience making bookshelves. You spend 50 hours making a beautiful bookshelf, and you carve scrollwork into the legs of the shelf and beautiful scrollwork into the front of each shelf, and it is level, square, and plumb. I spend 50 hours making a bookshelf, but it has one leg that is much thinner than the rest, and there is no scrollwork because I don't know how to do that, and I didn't really measure anything, I just kind of eyeballed it, so everything is out of plumb and out of square, and the bookshelf is rickety, at best.
According to the labor theory of value, our bookshelves are worth the same amount, because you put 50 hours into making yours, and I put 50 hours into making mine, and we have the same prior experience.
Another follow-up question, then: How did you manage to spend 50 hours making it? Did you sit there, painstakingly, making one leg thinner than the rest for some reason? Did you sleep? Did you spend 20 hours of it browsing HN? In either case, this would likely fall under the category of unproductive labor: https://en.wikipedia.org/wiki/Productive_and_unproductive_la...
There's also the distinction of "socially-necessary labor", which feels (to me) like Marx's parallel to subjective value - the more socially-necessary, the more valuable the labor (a nice table vs. a crappy one).
In any case, the value is not just a measure of "hours put in" as you're making it out to be here; clearly I put more labor into it than you if mine looks/performs better in the same amount of time.
